I mean, yes this would work in theory, but you also run the risk of ruining 2 controllers this way, if you have 80$ to experiment with, go for it. If I was going to risk ruining 80$ of hardware for something that was going to most likely end up looking unprofessional/glued together I'd probably see what 80$ worth of third party hardware would buy me... like an adapter. I think those adapters run somewhere around 50$ and up.
Alternatively you could just play with the 360 controller.