Been there and done that (except I kept all the sweeties to myself and didn't share).
I try to keep a bar (in addition to the fast acting glucose) of some sort with me to eat when I finish my exercise. If my BG has dropped a lot, I eat it without any insulin and test again when I get home.
I say "try". The problem is, I sometimes forget. At least I walk to the gym so not in charge of a car when going hypo.
I hope this doesn't put you off your aerobic sessions: despite the post-gym hypos, I feel sooooo much better after exercise than when I veg on the couch. I think it's endorphins or something.