Yes you will have troubles. Your ten speed cassette won't fit on a hub that is made for a single speed track bike. Nor will the wheel have the needed dishing of a road bike wheel with 10 speed free hub.
If you need wheels, then you'd do well just looking for your best deal on a wheel set for bike that supports a ten speed cassette. If your bike is a mountain bike, look for mountain bike wheels. If it's a road bike or one of the many sub-genres, then look for road bike wheels. Call or email the vendors if you aren't certain what will fit your bike. They'll help you if they want your money.
Try a LBS (local bike shop) They might find some inexpensive wheels for you. It was about twelve years ago, but one close by got me a wheel set for $90. Not bad for the POS bike I was riding back then.
Welcome to BF!
Last edited by Iride01; 02-19-24 at 10:48 AM.