If I have 2 (or more) ships, and one gets destroyed, do I have the option to not rebuy that ship, but instead merely switch to one of my other ones?
I'm afraid you don't. Your choices are re-buy the ship with all modules, re-buy the ship with slightly less components, or go to a Sidewinder.
Whatever option you pick you'll end up back at a station, typically the one you last docked at, and if you want to switch ships you'd have to transport it to your current location or fly to it.
Source: Brutal, gut-wrenching experience.