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Get a multi-tool no matter what your immediate plans are. Had a mates old Fein 1st gen tool and never looked back. Super useful, you'll find it always plugged in near you with a bag of blades sat waiting to be swapped in. Like yesterday was using it to tidy some plaster, cut a hole in a kitchen cabinet, cut some timber to length to reinforce cabinet, shave a bit off a few metal worktop brackets and then trim my waste pipes. With one tool, didn't even have to get up to reach the bag. Buy one*
*Yes using a multi cutter for wastes, I know I know. Did I mention I didn't have to get up though? :P
As for SDS prob overkill for tiles, just get some gloves and goggles and a bolster and go to town. Have an older Bosch blue battery SDS of a decent size, needs a battery again (goes months without use is probably the cause of failure), and if I need something really big a mate has a commercial sized Hilti. If its worth lifting the damn thing, its worth using, honestly even blue cobbles in walls it'll munch up, absolute life saver. Had to open up a few fireplace a few months ago and it turned it from an all day job into a 1.5 hour job.
It might me worth trying a multitool to get below the tile and a cold chisel to remove. That shouldn’t cause much damage at all.
I’m all cases remember GLOVES AND EYE PROTECTION!!!