You might as well try removing some of the old finish just to see how easy or difficult it is to get off. If you give up on the stain idea you have not harmed the shell, just wrap them. The quality of the finished product will depend on how good the bare shell is before you apply stain and finish. So you might consider stripping the smallest drum to see what you will have to start with. Problem is with the stain finish, you will really need to find your floor tom ( if thats what you want) and make sure it has the same wood as the rest of the kit.
Nothing wrong with wrap. As mentioned you could buy a piece for the floor tom for later on when you do find one. Wrap would be the easiest choice for you and the drums will look spectacular with most any of the new wraps. And it will still be a great summer project. There is a lot of work taking them apart, cleaning all the parts ect. Whatever you choose keep us informed we love looking over the shoulders of our fellow members. And we will be here to help out when needed.