It is true that the MAIN reason for removing water from potatoes when cooking them is to be able to achieve a crispy, browned (and consider that "browned" usually means "more flavorful") end product.
But it is absolutely not the only reason. A secondary reason is cooking time. Oddly, boiling them in water that never passes 212 °F will take less time than baking in a 350 °F oven. But given that one is baking them, not boiling, frying, or microwaving them, water is not your friend because so long as they are quite water-filled, and potatoes are something like 80% water, they will be limited to boiling water temperature or less in their cooking mass. And since the water in them is not boiling, and much evaporates, not steams, the temperature of the water pervading them is nowhere near boiling, en masse, as it would in a pot for mashed potatoes.
Remove enough water and the worm begins to turn. The water in the not-on-top layer can reach higher temperatures and the top layer can lose enough water to crisp and brown up.
It's a matter of quantity. Over a point, the quantity of water in them simply overwhelms the situation. Go below it and you have more acceptable results. Go below enough and you have great results. WHERE those points are depends upon your exact potatoes, but shouldn't be too important, and your definition of "acceptable" which is entirely up to you. However, the monkey wrench in things is the other foods cooked with them.
Their cooking times until "acceptable" for all players must be more or less the same. More of the more, and less of the less, so perhaps "essentially the same" is better.
Squeezing is an old wheeze and not really doable in most peoples' situations. The grating operation should be performed and then multiple "wrap in tea towel, squeeze in a manly way" then let rest and repeat a few times method is the only one that really works. Crushing down in a colander/sieve isn't usually hugely effective as most people don't keep them from moving instead of squeezing, which the tea towel method accomplishes pretty well as a matter of course. On the other hand, a big ball in the tea towel rather than a cylindrical and twisting squeezing operation can be less effective than a well done colander/sieve approach. It's just most people don't have "tea towels" (non-shedding towels one devotes to such things as well as using them as awful potholders). So the colander/sieve approach.
Whichever of those two though, one needs several stages.
A microwave can do more than just cook though. Many are familiar with the idea that "waving" an orange or lemon before squeezing gets more juice out of it. Same thing with potatoes. Spread them on a plate, fire up the microwave for, say, a minute, and let them sit afterward with the microwave door open. (Or not... you can wipe it down after, and with the food (potatoes here) not cooling down in the room air, more water can be removed.) You can underlay them on the plate with 5-6 layers of paper towels if you don't use the horrible kind that are a cross between tissue paper and newspaper. "Pillowy" I think would be the word for the right kind. Or on a tea towel!
If cooling in room air or with the door open, blotting with and leaving on a top layer of paper towels (or a tea towel) will help take away the water.
Then repeat a time or two or until it doesn't do as much one time. But not enough to cook the potatoes significantly. The cookbook writer probably ("maybe," in the sense of "60% of the time it works 100% of the time") tested the recipe and if prepped accordingly it really does bring all the pieces together at the same moment.
After "waving" them, you can definitely try the squeezing, for the same reason as the orange/lemon, though the release of liquid might not be as much as in them as they were "waved" in a sealed container, not on an open plate (unpeeled, in other words, whilst the potatoes are definitely peeled).
Either way, squeezing or not, the microwave can be your friend in more ways than just cooking.
Another approach is to allow them to sit, after some step like the above, in a colander/sieve and drain, then to repeat one's earlier step.
As mentioned in barbecue's comment, the heavy weight on them whilst either just wrapped or in a colander/sieve approach can work. It's all a matter of the amount of time one has. More time? A less strenuous approach might be good. Less? Well, more work is required, and when more work is not helpful on its own, assisting it with a microwave expanding the water by heating and driving it out of the food is a way to add "smarter" to the mix.
Bear in mind that removing all the water is not only not possible, but you are going to add wine and cream to ingredients that are not, themselves, unwatery (the peas and cod). The key is to reduce it "enough" and that level will depend solely upon your own circumstances. Your oven's characteristics, those other ingredients particularly the water containing ones, and the potatoes you use themselves.
However, all that said, for the potatoes to really crisp up, the loose starch on them needs removed. They need rinsed, and soaked for further rinsing, until the soak water stays mostly clear. THEN they go through the above kinds of approaches.
More caveats? Well, you never want to crush to the point that you break the potatoes up too much more than however you grated them to start with. Nor do you want to remake your potato with all the crushing. No crushing until they are a new solid and more would make them diamonds. This is part of why you need to do it several times... you want to be closer to "gently crush" than to "wrench them like a stuck wheel lug"... This is also why you don't place them on a couple tea towels and take a rolling pin to them. Paper towels? When I say paper towels, I seriously mean plural. Not the silly one paper towel people put onion rings on to drain. 5-6 of the thicker, pillowy kind is a minimum and if using them as the squeezing medium, then MORE, and probably changed and more squeezing done. They have to take away the water or there is little point to the squeezing. That was why that blotting and leaving to absorb further evaporated water in the "microwave on a plate" suggestion. And why an underlayment of them. Commercials lie like rugs. Paper towels do not soak up gallons of liquid each. (Nor do tea towels (especially as most tea towels are actually cruddy as towels, nothing like terrycloth at all, just useless for drying dishes for instance), so be sure to wring them out too, and "repeat." Their value is physical strength (no tearing apart when wet!) and absorption mass.)
Personally, I would not microwave with the goal of cutting off those ten minutes of cooking time as the still quite moist potatoes may end up cooked well at the same time as the other ingredients, but two other things would obtain as well: the liquids (the water in them at least) you added will not be absorbed into the potatoes as much as they would have been were the potatoes less moist so the "bottom" might be far moister than desired, and the flavors from them more intense, perhaps "sharper" being a better word considering the wine, in the peas and cod, mostly the cod, and less than desired in the potato layer. But then, you might actually prefer that, personally, so something to think on.
Experimentation is the real solution. The cookbook and websites like this only get you near the goal, unless luck is your specialty. You then have to bring it in to your taste. Or your family's. Unless the recipe ends up near enough to make you happy, of course.
