FYI, if you order a tea at the Café Fantasia in the
Disneyland Hotel, they bring you a cup of hot water and a separate tea bag. I believe you have a chance of not getting charged if you ask nicely only for the cup of hot water (especially if you pay for something else) but since you mentionned you would not mind paying for it, I thought you might like to know. I believe the Café des Sports and Café Ludwig do the same in Disney Village.
Also, I know you did not suggest it, but for the sake of the discussion, I would like to mention that I would strongly advise using hot water from any of the lavatories, since only cold water is drinkable in France (As I believe this is the case everywhere around the globe though you never know, better be safe than sorry.)