You could look up a local place on Yelp, then take an Uber or Lyft. Still that will add to the cost, so consider that. Plus added travel time.
Maybe just splurge at a Disney resort, since you are on vacation!
I do gel manicures, so here at home a mani/pedi (French on my hands) runs me $60 plus tip. So, I'd figure if I were on vacation and added maybe $20-$40 on top of that, heck, it's vacation. The thing I don't like about getting my nails done on vacation is taking time away from relaxing at the pool or something!
I'd just go ahead and splurge. I got my hair cut once (many years ago) at the Grand Floridian. It wasn't more than at home from what I recall.