IMO, it's never a good idea to place a wet fly in a fly box with other flies. That's a good way to get rusty hooks. I usually stick them in my hat, ( debarbed hooks of course) or if fishing from a watercraft I have a foam block I stick them in to dry. A drying patch is a good idea too.
You can quick dry them with silica powder, which is or at least used to be sold for drying dry flies. It's simply a finer form of silica gel desiccants, which is used to keep moisture away from a lot of things. If the fly is too large to fit in the container that the powder comes in, then a larger container would be needed.
I save those small bags of silica gel when I get them & keep several in fly boxes & boxes of hooks to help prevent rusting.