single handle shower faucet sticking - can I fix without turning water off?
That is a Moen brand shower valve. It has a cartridge (plastic or brass) that inserts into the valve body, retained by a "U" shaped clip. The cartridges get sticky over time which can be remedied with waterproof plumber's grease but I would probably replace the whole cartridge.



The water needs to be turned off but you may be able to do it right at the unit. Smart builders/plumbers frequently install shower valves with built-in shut off valves, for apartments and condos. These are called "integral stop" valves.

Remove the knob and trim plate to see if there are integral stops on the hot and cold water supplies, they will be a part of the shower valve and will look something like this:



The small stems with the slots are the stop valves, which can be operated with a screwdriver. If you do not see the integral stops, the main water supply needs to be shut off prior to servicing the cartridge.