Jeremiah,
I agree with Kraig. The drive cup on the flywheel should be the only difference. I am not familiar with the gear drive cup, but the 125 hydro will use the slot cup with the pin on the driveshaft (the one that likes to waller out the drive cup).
We have contemplated doing a similar swap of a 127 engine (narrowframe hydro) into a 129 (wideframe hydro). On this one, all we would have to do is unhook the driveshaft, disconnect what is left of the electrical that is connected (I got it in a deal with my 1650 and all the attachments I got last spring, and it has issues, biggest being the hydro dump lever is stuck straight down, the hydro direction lever is frozen in the neutral position, the brake is stuck in the "on" position, and you can push the tractor with little effort) and remove the tank and mount since the 129 tank is on the dash, not the engine. For yours it should be disconnect electrical, pull engine, swap cup, reinstall engine, connect electrical, enjoy 125.....