When you are applying snaps through only two very thin layers... like when you are making a PUL diaper or a thin flannel diaper... Nail clippers are your friend!
Insert your cap through.
Snip off just the very end of the point so you're left with the flat post.
Apply your socket or stud.
Press as usual. I only have pliers, so I have no idea if you need to do anything with a press.