Hmmm. I don't believe that FE has an electronic shutter. I am pretty sure (actually, I'm certain) that the shutter in the FE is mechanical. I think that it is the same shutter mechanism as the FM. The FE2, however, has an electronic shutter. The predominant difference between the FE and FM is the FE's auto exposure mode. I don't have an FM any longer, but I have 2 FEs and an FE2 and I can snap the FE shutter just fine without a battery in it. At any shutter speed to boot. The FE2 (just like my FG) must be set to M90 or B to release the shutter without a battery.
I am corrected.
FWIW, All of them have a mechanical shutter, but not the same shutter. Some(FE,FE2,F3 etc.) have Electronically controlled timing circuits. The electronic variety uses coils to control the timing.
The one thing they all have in common is that they are released by the mirror reaching the top of it's travel and releasing a lever actuator.