the wings won’t hurt anything, i wouldn’t bother to try to get rid of them. stratification is mimicking a normal winter cycle. sometimes it makes sense to plant them in small pots and then bag them and stick the pots in the fridge for a month or 3. in this case (and assuming you’re somewhere that gets a decent amount of colder temps in this season), i’d plant them in pots and just leave them outside where they’ll get rained/snowed on, frozen, etc. maybe on the north side of a building so they don’t heat up too much on real sunny days. let the weather do all the work. i sometimes do a little extra rodent protection on stratifying pots but i probably wouldn’t worry about that in your case unless your
mice are really out of control.
if you wanted to wait to plant until the spring, that’s when a 24hr soak would be most helpful. you’ll get
enough ‘soaking’ in the freeze/thaw cycles of stratification though.