* If you mean can you replace the battery and keep using the same fob: Yes, absolutely. The key fob itself is a simple device containing a battery and a transmitter. Replacing the battery is a common and easy fix.
* If you mean can you use a key fob from a different year Corvette or another GM vehicle: No, likely not. While some GM fobs might look similar, the frequency and coding are likely different, meaning it won't work with your car's receiver. Each key fob is programmed to a specific vehicle.
* If you mean can you buy a replacement fob and program it to your car: Yes, you can. You'll need to purchase a new fob specifically for a 1999 Corvette (or one that's compatible – check with a dealer or reputable online parts supplier). Then you will need to have it programmed, either by a GM dealership or a locksmith specializing in car keys and fobs. This usually requires special equipment.
In short, you can replace the *internal* components (battery) of your existing fob, but to replace the fob *itself*, you'll need a compatible replacement and programming.
