2 weeks where one's autonomous transport range is cut to between a quarter and a third of what it was seems like a big deal to me. It's bloody annoying if minor medical procedures result in a significant minority being advised in effect to pay for loads of taxis or hire a car for weeks on end (only an option if they hold a current driving licence in the first place)!
Seems a little unfair to quote me to make this point, but trim off this
This seems OK. If the problem is sweat, then don't exert yourself. If you work at about the same pace as brisk walking, you shouldn't have sweat running down your back.
I was crediting the OP with a little intelligence. If I was told not to ride my bike because sweat would be bad, I would either assume that I could ride gently as transport or ask a followup question if I was not sure. As the OP didn't do this, I assumed all his rides are workouts, and wasn't interested in riding without sweating.
When I broke my wrist (not on the bike), I asked the specialist if I could ride. He said "You could, but I wouldn't want to think what might happen if you came off." That gave me all the information to make a decision, that for me was TFL and walking, as I couldn't drive with it either.