Simplest solution would be to take all the electric-start components off the parts motor and transfer them to yours. You can use a hole saw to drill a hole in the Starboard side of the lower cowling, to mount the electrical connector (also needs 4 holes drilled/countersunk for the mounting screws).
If your Short Shaft 50hp doesn't have a flywheel with starter teeth on them, just swap flywheels. You'll need a flywheel puller for that job, but they're not too expensive. An automotive harmonic balancer puller with Grade 8 fine-threaded puller bolts will easily remove the solid flywheel. I can't recall if they're 1/4"-NF or 5/16-NF but it's one or the other. You must use Grade 8 or better bolts, else they'll pull out of the flywheel bolt hole threads and make a big mess to deal with.
The starter motor/solenoid will transfer over easily, and assuming the donor 50hp has a charging system, you'll want to transfer the stator and rectifier as well. Plus the electric choke assembly.
Does the donor motor with the bad lower unit even run? I wouldn't do a bunch of powerhead swapping work unless I knew that the other powerhead was in good running condition.
Failing all that, you can pull powerheads on both engines, swap lower cowlings as appropriate, and re-mount as you wish. The '66 and the '67 use the same powerhead base gasket and exhaust plate gasket, so it's just 2 gaskets, a rubber grommet, and a bunch of wrenching on 2 powerheads to get the job done. If they're fresh-water motors, they'll come apart easily.
www.marineengine.com/parts/mercury-outboard-parts/500/2116318-thru-2305100-usa/bottom-cowl-assembly-and-shift-linkage
IMHO, I'd take the best of both motors and make one good one.
HTH..........ed