Thanks all. I had been thinking about pulling out a hair dryer, but that sounds like a bad idea. Especially now that it's gotten cold, and the car sits outside.
I'll poke around with a razor or the suggested fishing wire. It should be clear pretty quickly how it will work out.
I don't have acetone (nasty stuff, I understand). Using a lot of WD-40 or Goo Gone just to loosen the antenna counts in my book as making a big mess, so that's out. It may be required when cleaning up after a successful removal.
Next step would be to remove the matching base and wire inside the car.
A '97 Saab 900 is somewhat GM, somewhat Saab. I don't know whether I should blame Saab or GM for an alternator placement and bracket design that requires hours of work by a Saab specialist to extricate after one of the alternator-to-bracket bolts seize and get stripped by a previous owner. Otherwise, it's a nice car, and for its age shows just about no rust--galvanized underbody parts.