I've made several small quilts where I pieced 10" blocks of minky for one side and used cotton on the other side with no batting in the middle. One of the quilts used a beautiful jungle print that I didn't want to cut up. These quilts look great with either side up.
Minky sheds A LOT! You will be sneezing Minky fluff for days. As I cut my blocks of minky, I put safety pins along the two stretchy sides. After I laid them out on the floor, I made sure that each stretchy side (marked with a pin) never matched up with another stretchy side. Worked great.
Regardless of if your quilt is pieced with cotton using minky as a whole piece, or using minky pieced and the cotton as a whole piece, I would suggest that you simply lay them out flat on the floor and safety pin the layers together. Try not to pull the minky taut.