I'd like to update the handles for the faucet in an existing soaking tub to something more modern than these knobs. Is it possible without taking out the tub?
You will surely be able to remove the knobs without removing the faucet valve body and without removing the tub.
First examine the tops of the knobs and see if there are caps which pry off to expose bolt heads underneath. Remove these bolts (screws) and then wiggle the knobs off. You should be able to find other knobs more to your liking that fit the same shafts.
It depends a bit on how old the valves are. You can get universal handles for valves that operate with 3 set screws and these handles could be used to replace the ones you have.
I've found non OEM handles tend to be clunky, are hard to install, and tend to strip the cartridges. My experience was with crane shower valves. Probably the best thing to do is to cut an access panel to the under tub area from the wall, remove the existing fixture and replace it with something modern.
You could go for universal replacement handles, see if you can find anything you like, try them out for a few years and when it strips the cartridge or you get fed up with the handles then go for the open wall or ceiling below and replace valve assembly. You should get a plumber in for valve replacement as soldering in confined spaces is when you get your value out of their labor.