#10-32 will run down just fine on 3/16" shafting.
#10 thread diameter is 0.190", 3/16" is 0.1875", just slightly smaller... and the threaded prop doesn't pilot on the thread OD, but on the flanks of the thread... no problem.
Put a 45° chamfer on the rod end first, which will ease the die into the cut.

Pat M