You can get baseboard heater covers. A baseboard electric element should withstand water splashes. In my experience, the bigger problem is cleaning products and urine. Another solution is to get a ring towel holder for a small towel right next to the sink. We have one crammed into a small space by the sink. It's convenient. (ps, this is not our bathroom).

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That's only three years of wear and tear? I would assume a new low profile would work fine. I might try and midigate the hand dripping issue.

FWIW: are you sure the dripping is the issue? That's a lot of rust. How humid is the room? You might need a stronger fan and dehumidifier as we do in the South.

I cannot imagine that rust only caused by drippy hands . Why not move the towel rack to start then use rust remover and prime well and repaint then see if it gets wet.It looks to me like an old heater was used to start Most new ones are much less bulky and more effcient.

Maybe look into Rust-Oleum to see if it could help resolve and also add a towel hook elsewhere, even on back of door if short on space.