That is an issue, but I can think of a few ways around it. An idea that occured to me is, if they got the Hannibal Lecter route (which I really hope they do), they can show the makeup-less Joker in shadow in his cell for the first few scenes that we see him. When the time comes that the police request information from him on Gotham's newest villain, he could cooperate on the conditon that he be allowed his makeup.
Or find some other reason that Arkham would allow him to wear his makeup. Perhaps he threatens to kill other inmates unless they provide him with a supply of facepaint?
Just not some really obvious, gimmicky thing, like he gets plastic surgery or something.