Can you change the game in a way that doesn't use the IP? There are many games that are clearly inspired by some IP (game, TV series, film) but doesn't actually use the IP (you need to do more than just change names of characters or whatnot).

Other than that, yes, you need to ask for a license deal. Depending on the license holder, this may be cheap or expensive, or you may be able to cut a more flexible deal rather than pay upfront (e.g. share of profit, but you're making a non-profit deal, so...). Or maybe you can make a deal to release it on their website.

Or just hope they don't notice...