The reason I pulled the head off the larger drum was because it seemed to thin for that drum. I was hoping to reuse it instead of buying a new head for the smaller drum.
Ah ... that makes sense. Well, if it was too thin for your liking on the large drum, it just be the right thing for the smaller drum.
If possible, don't trim or cut the skin in any way until you know for certain that you want to use it on the smaller drum. You don't have to cut/trim until the head is mounted and you hear what it sounds like. It is easier to trim before the skin completely dries, but if you do that you'll be stuck using the skin on that size drum, even if you soak it again.