Many people have said they are going to do this. To date I have yet to hear of of a successful swap. I think that once you get both apart you will see the level of modding you will have to do and decide it won't be worth it. But if you do it, make a guide along the way.
I wanted to swap the 3n1 into the translucent black cover that came with my DX case. I have swapped cases on my Wii, Wii remotes and nunchuks, Xbox 1, PS2, and my DSLite but I gave up the the 3n1 to dust cover swap.