In this recipe, can I substitute or do without the white wine? Is there a non-alcoholic substitute?
Why substitute anything? Cooking is all about tasting, if you like how the soup tastes without the wine then there's no need to add anything to replace it. The white wine supplies acidity, which you may not actually want if you've already added sour cream. It also supplies fruitiness which again may or may not be to your taste. If you want more acidity then squeeze some lemon juice into it, if you want fruitiness add maybe 1/8 cup of white grape juice. Add a bit at a time, tasting as you go to make sure you don't overdo it.
If you decide you like the soup without the wine then don't add anything, your recipe won't miss the 1/4 cup of fluid.
Consider using white wine vinegar. The flavour profile obviously isn't the same, acetic acid changes things a lot, but you do get the other flavour compounds you get in wine.
That said, subjectively speaking, I agree with the suggestion of lemon juice to go with fennel and sour cream. Or maybe a combination of the two.
The amount, 1/4 cup, is so small that it probably doesn't affect the final flavor too much. Easiest substitute would be low-sodium vegetable stock.
Some commercial vegetable stocks do contain trace amounts of white wine, so check the ingredients in the nutrition facts if this is a problem.
I'm in the same boat. I've tried vinegar, stock, water, orange/lemon/lime juice, etc. many times, but never been happy with the results.
Meier's Juice has a nonalocholic Chablis (dry) and Spumante (sweet). I think this recipe would probably use the Chablis. I've used both of these as wine substitutes for years with great results, and always have several bottles on hand.