Move to a warmer climate where condensation is unlikely to form.
Generally temperatures above 24'C (mirror ambient temperature) are suitable. You just need a surface warm enough and vapour pressure right for there to be no condensation. I found in Cairns I had NO condensation and could shave while having a hot shower.
Personally, I do the 'by touch' method. I've found that I am fairly unobservant when it comes to shaving, so I am better to go by feel, let someone tell me I've missed a spot, go back, re-shave, to get that same person to say, nup, missed it again, to go back, re-shave, return to the person who will inevitably say, what, are you blind? To me asking them to come point to the missed spot and keep their finger there until I get to the mirror.
So far, I've had no issues with my current methods.
OH - NEWS FLASH!!
OMG... I didn't read your mirror was in your shower? Is it as big as the one above your bed?
Anyway - Had a BRAINY idea...
OMG... You'll LOVE IT!
Sax... You so gotta do this...
Suggestion!
Go to a wreckers, pull out the wiper motor from a dead car, get new wiper arms (because that would be dirty otherwise) and new blades, get a 12V transformer (because you really don't want a car battery in your shower and live electrical wiring is usually fine). And voilla!
To be honest, this would be possible. You would want a fairly secure place for the transformer and wiring, but there's no reason it wouldn't work!