i Think
@neil_w is more of a “put the glue on the fin first” as opposed to those of use who “put the glue on the paper first” camp i hang with.
if you are in the latter camp, a trick that may make it easier no matter what adhesive you use.
get some throw away magazines for mail order catalogs.
lay your cut out paper intended glue side up on the front cover.
apply your adhesive of choice on the paper, mainly in the center,
use a hotel key card to squeegee the glue from the center to the edges, you want a smooth thin even coat. You may need to keep a finger on the paper to keep it from sliding around on the magazine.
once you have the paper coated, lift it off carefully (white and wood glues will makes it soft fast, so work quickly and be gentle, sometimes if use the back of an 11 blade to get it started.
once you lift it off, flip the page over, you now have a clean surface to work with to skin the fin. If it gets some glue on it while working the paper onto the fin, flip the page when done for the next paper piece.
may not qualify as recycling, but at least repurposing something you are gonna throw away anyway.