No shower would be a deal breaker for me. even with a sink wash and baby wipes I amd uncomfortable and get sore well hmmmm 'parts'
In terms of solution
1. try and get a shower installed
2, join the local gym/leisure centre and use their showwe maybe.
How does a shower cure sore 'parts'?
I think people are obsessed with showers. I don't believe a shower removes sweat anymore efficiently than a sink wash with a flannel. I think a lot of people
like showers, and tell themselves that they are essential.
Me and the boss ride to the office (him 5 miles each way, me between 3 and 10 depending on how energetic I feel). We don't shower, and I don't notice any problem. We don't race in, just ride at our comfortable pace, and we're rarely sweaty when we get in.
At the other job of course, any sweaty smell is the least of our worries, compared to the recycling boxes. Sweat is fragrant, compared to week old Carling-mixed-with-off-milk.