Epoxy could work.
3DSs have their interconnect ribbons in the right hinge, the left one is 'just' the mechanics.
Also, the shell is pretty sturdy. But nevertheless, you really should replace it, but probably enough just the inner shell of your screen to replace.
Now the sad part is that IIRC for that, you still have to disassemble the whole unit - including removing the ribbons in the hinge then reinserting them. This sucks major ass, it's really-really hard and tricky to do, and there's a relatively great chance you bork some of them (camera, screen or speaker/vol/3d controls).
It's not impossible, tho.