If you have all the pieces, you could use a good grade fine epoxy, gorilla glue, or a gel Super Glue (must clamp any of
these for it to be effective). Or just put some electrical tape on the splines, just enough so the reel will fit real snug. Actually,
I recommend getting a better projector, since the Whisper is a Dual 8mm configuration using the pull down claw to do all
the work rather than having a proper sprocket to run the film and thus relieve the additional stress on the sprocket holes. I mean,
it works fine for a couple runs or so, but I wouldn't want to put lots of wear on any film with this. It's gentle enough, but this is a
cheaply made projector. The only things going for it are dual 8mm, quiet running, and variable speed (for cheap film transfer DIY).
You'll be much happier, have better results (brighter, sharper, steadier image on the screen), if you opt for something like an ELMO.
Just my two cents here.