The overflow shouldn't be a problem - it comes off with the drain to the tub. The biggest problem may be the size of the drain. Code requires a shower drain to be 2"; a tub is normally 1.5". Now, your pipes may be 2" with a reducer to get to the tub fitting, but if it is 1.5" to the stack, it won't meet code, and you could have a big problem with the inspector and with performance. A tub has the large depth to keep water from backing up and spilling out onto the floor. A shower typically does not. So a restriction or clog can get really messy quick. Note, some companies sell those things with 1.5" drains, but that does not mean they are legal to install.
You'll probably want the shower controls higher than the tub controls, but that should be fairly easy and straightforward. Note, again, though, that the code requires the new valve to be a pressure balanced or thermostatic/pressure balanced valve to prevent inadvertent scalding.