Older model ISE units didn't use a magnetic stopper but just a mechanical one. The ISE stopper part # was 1019-C and there was a KitchenAid version part # 4211474. Both appear to be discontinued. I'm afraid I don't know where you'd find either.
You could check with a local ISE service depot. They might have a used one still kicking around from a unit that was scrapped?
LINK > ISE Service Depots
The only other options I can think of is bypass the on/off switch and install a wall switch instead as Rick said. You'd then need to find some type of stopper to cover it while in use. Either that or replace the whole disposal with a new unit.
There are several ‘batch feed’ disposers still available.
LINK > Batch Feed Garbage Disposals
Dan O.