One of our favorite projects from last year is the illuminated etching by Lee Pembleton. The artist meticulously cut out two sections of the etching and placed colored paper behind the incisions creating depth only to be flattened by the frame's backing. Our friend asked if it was possible to light the separate areas of the etching and we said maybe.
The result was a compact LED light assembly housed within the backing that runs on two regular 9 volt batteries. This would nix the 'cheese factor' of a cord-to-outlet but the batteries only run straight for less than a month. A switch is possible but it would detract enough and creates maintenance. Add museum glass to the mix and it becomes a little risky handling the frame too much; museum glass is porous and it's difficult to entirely remove finger prints once they're there.
As I'm writing this I believe it's possible to solve the battery problem with a little more research and a small design modification. The only way you get better is to guarantee your work.