Is it possible to have alternate bound weapons of a particular type, and control which one activates based on a script?

Yes, to some extent.

You'd need a scripted spell to handle summoning. Then use a timer to keep track of how long the weapon should be around for. When the timer runs out, remove the weapon from the player.
If the player un-equips the weapon, you can re-equip from the timer script to handle that part, if you want to force the to keep it equipped. You could also just remove it from inventory if it's unequipped.
To keep them from dropping it, you'll need a script on the weapon to Disable and SetDelete itself when the PC drops it.