Yes, you can paper an entire balsa sheet and cut the fins out of the sheet.
I have tried this with regular white glue, with glue sticks, and with spray on adhesive on 6x36" sheets of 1/16" and 1/8" balsa. All work.
The wood tends to warp particularly with white glue, but with the others a bit as well. You need to do both sides at once (a bit tricky.) I put the glue/adhesive on the BALSA first, then put the paper on, then smoothed it out.
I bought two four foot 10x48" shelf boards and covered them with wax paper. Once I glue the paper on the both sides of the balsa, I stick the whole thing between the two boards, set it flat on the floor, weight it down, and let it dry for 24 hours or more to prevent warping.
Once you start cutting it, make sure you keep track of which way the GRAIN is going on your balsa, once things are cut out of the rectangular sheet, can be hard to remember and isn't intuitively obvious.
The fact that you have to do both sides at once, and kind of fast or you REALLY get warping, makes it a bit challenging.
I've had a few cases where the paper peels back at the edges after cutting, I think likely due to not getting a complete even coat of glue on the wood in the first place. Might be a good idea after cutting but before sanding the non-root edges to take down the edges with thin CA. Some recent brilliant TRF'er (can't remember who) had a technique for putting the CA on a surface and using the edge of your fin to swipe across it, to give a very thin non-drippy "edge" of CA along the margin of the fin. Only works with straight edges, though.
edit, how could I forget K'tesh. Here is the post on the edges
https://www.rocketryforum.com/showt...-Fins-A-foolproof-method&highlight=glue+edges