I dried some cavatelli I made with egg dough (I know it's usually made with AP, semolina and water but I was improvising), however, I had to add some excess flour around the shapes to prevent them from sticking during the drying process. I'm reluctant to cook them with the flour stuck to them so as to prevent the dreaded gummy layer from forming on the outside of the pasta. Should I wash the shapes when they're dried? What's the best course of action? Thanks.
Brush the flour off using a soft cooking brush (or even a clean paintbrush). It might take a while, but as with making pasta itself, it's a slow and involved process which eventually gets faster. You might want to consider doing this over a baking sheet with a wire rack.
I would not wash them up!!!
Since it is not a fragile pasta shape, I'd put them on a baking sheet (or a bowl) and shake them, the friction and collision with the other pasta will rub off the excess flour.
You could also use a colander or a sieve.
I'm not certain why you needed to add up more flour when you dried them up?
Rather than drying, you might consider freezing your hand made pasta. You can freeze them flat on a semolina or flour dusted plate or pan. Once frozen you can store them in freezer bags. This will allow you to use less flour in the first place, but, in the event that you've used too much, once frozen, you could get rid of some of the excess flour by shaking them in a strainer just before you put them in boiling water.
I'd do with a mix of what's already been mentioned: let it dry, then put it on a sheet pan or strainer and shake to see what you can get off that way (strainer will help more with surface flour, but not the stuff in groves). If it's still bad, use a pastry brush or similar.
And one other possibility to help with the "gumminess" ... when you're ready to cook it, give it a rinse in a couple of changes of cold water (but it needs to be really dry for this, so it just washes off the loose flour), and you need to get it into boiling water immediately afterwards