i cycle or run the 10 miles to work.
i have showers but used to have to use the sink,
take a flannel soaked in shower gel,use a swimmers absorbant towel.
i keep my shoes and pants at work and take a fresh shirt and undies and socks every day in a bum bag.
when i run to work i ensure that when i get there i have some fluids to down asap or carry a bottle in warm weather.
pace is the key,if your steady enough you wont be as smelly