Two LiFePO4 14500 in parallel is good idea, and I need to modify the cell ways
Note that the motor is still likely to be a bit overdriven (though a lot less than with a LiIon cell).
Also, never put in parallel two cells with different charge levels; if unsure, just use one.
I'm not quite sure what advantage you would get from changing the battery supply?
The way I see it, being that the shaver is old and most likely has a direct connection from the battery to the motor, using NiMH would make it go slower than on alkalines due to the lower voltage (I don't think a shaver draws enough current to slump the voltage of primary cells much).
A pair of LiFe cells would be the best of both worlds, as they'd get you a slightly faster motor and the ability to recharge them.
If performance or run time seems excessively poor, it may be that the gearing and bearings just need some cleaning and lubrication
That is, of course, always a wise thing to do to old equipment. Cenz, I recommend you do that in any case.