I'm not aware of any differences in the light truck (F100-F350) cabs that would prevent you from swapping them but I've never actually done it. The only difference I remember seeing is that some of the larger truck (e.g. F-750) cabs had an access panel in the passenger's side floor for the battery. Those might have other differences I don't know about.
You will prolly want to yank the whole harness out anyways. Great time to look it over. None of the wiring is specific to the cab. As long as you switch all the doo-dads as well, you will be fine. I used a '59 F500 for a parts vehicle and that was identical to add to what manglass what saying!