You are the first person I have ever heard of that is concerned about covering skin because of riding a bike.

Since you are showering at work, that means you have the opportunity to wear whatever you find best for your bike ride, and then change into whatever you wear for work. If you want to wear khakis and long sleeves on the bike, that's up to you. As others have said, you'll have to get pretty fast for clothing to make a meaningful difference in your speed.