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Judging from my own cheapo stick it’d probably take a little bit of doing. You’ll be stripping out the buttons/stick/board inside, just for starters.
If you need to expand the holes like Gahrling suggested then it may make it a little trickier if you’re doing it diy style.
If you like the box though or don’t wanna buy a more expensive box I don’t see why you couldn’t do it though, may just be a pain haha.
If you have a few dollars though I’d look into one of the boxes Gahrling mentioned or even have a look in some of the other threads, there are some decent looking perspex/plexi boxes that someone makes/sells, would link it if I knew where haha.
Alternatively find out if there’s a makerspace/hackerspace in your area with a cnc machine/lasercutter/3D printer and make your own
Edit: Found him, more pictures in the thread, didn’t wanna spam image quote, just wanted to give you a preview