If using solvents, rubber is very easy to remove, the problem you may have is removing painting or finish on a gym floor, and I'm not sure how a gym would react to spraying any thing on a floor any way.
WD-40 would actually be my first choice to test - it works well at softening rubber, does not leave a lubricating residue, and is pretty safe on most surfaces, oh, and it is cheap.
I'm not sure if alcohol will help (never tested it) and acetone could remove the finish of the floor, and I think both of those smell as well, which would be bad.