I've got 12" 5 lug steel spoke wheels for my little 8' utility trailer and the spare tire I have for it measures 10.25" at it's smallest inside diameter where the center section of the wheel is welded to the outer rim part.
So, if your brake drums are actually 10" dia at it's widest part, they should work..
But, I think the actual 10" is the inside dia of the brake lining isn't it?
I just checked the 13" wheels I have for my TT that has 10" brake drums on it and there is approx .5" space between the wheel and the drum..
So, it'll be close for sure! Maybe get a set of 13" wheels and the smallest tire they make for it?? My 175/80/13 tires are ~ 24" tall, so maybe not enough to clear, but let a little air out of them and you might get that extra inch?
Good luck!
Mitch