I looked at several catalogs for you.
Crossdraw holsters without snaps or straps are not common.
Here is one.
https://www.mernickleholsters.com/sh...ter-p211257306
Andrews and others have cross draws with thumb breaks that will not slow your draw if you practice with them. The lining covers the back of the snap.
http://www.andrewsleather.com/traditional.htm