Epoxy is going to be your best bet, unless you plan on replating.
You can usually melt the solder on endcaps enough for them to come off without scorching, but re-soldering them back into place will almost certainly leave them scorched, because the cap just doesn't have enough contact with the rest of the razor to transfer all that heat.
Thank, AMB. I was cleaning it after using it for a week and as I was giving it a once over with a soft tooth brush the end cap just popped off. I'll let it dry and try a couple of dabs of marine epoxy.