What other games does your cousin like? Are you introducing them to Monkey Island because of your own nostalgia, or because it's a game that fits your cousins tastes?
Theres nothing wrong with trying to broaden their taste, of course. But they're gonna have their own tastes, and it wouldn't be fair to impose on them.
So ask with an open mind, and take no for an answer. Don't be pushy if they refuse. Its OK if they don't want to play it.
In terms of graphics, just show your cousin some screens and ask what graphics they want to use. Its for their sake after all. Do play a version with voice acting, though. Unless your cousin just really hates voice acting for some reason. The VO work really elevates the dialogue.
You could also just slip a bunch of your retro games on their PC as a gift and see if they go for it. Why not give them a copy of your entire retro collection, even. If they want it, of course. I got some of my games as a kid from hand me downs, and I didn't mind that.