First - you can use anything in a quilt - think back to all the quilts made from whatever the people could find. If you are worried about different shrinkage, wash everything hot and high dryer heat - shrinkage will be complete. Then, if the squares are big enough to be concerned with stretching, use a lightweight fusible stabilizer similar to one you would use for a T-Shirt top. If the squares are 'regular' size or smaller, the quilting will probably hold them in place without using a stabilizer. Quilts are to be fun to make, to be creative, to try new things. The worst case scenario is that you absolutely do not like the result, so you donate it - someone will treasure it - so it is still a win-win.