The OP is already risking dropping a razor in the shower, so is not averse to a calculated risk.
I see battery powered heated mirrors made for the shower.
Hey, I use an electric toothbrush in the shower.
I also use an electric toothbrush in the shower.
The only time that I have ever dropped a razor
was when I was changing the blade on a three piece
in the shower.
That gave me an insight to a post by a three piece user
asking about how well a one piece would survive being dropped,
which was, from my experience, a hypothetical question.