Just do it
.......you'll be glad you did. I bike to work every day at 14 miles round trip and I love it. There are no showers where I work at either, but that is'nt an issue for me. My locker is the two bottom drawers of a filing cabinet, and in it I keep my clothes, work shoes, deodorant, cologne, and packs of Old Spice refresher towels (those are great). Eventhough I always ride in sweaty, I amaze the people I work with because I can "shine up" like a new penny and look fresh as ever. I work nights and usually carry a back pack that houses my SLA battery for my bike light, and my "nextel" phone, plus whatever clothes I carry. All this works great for me, and it will for you too. All you got to do is just do it.
I always shower before I ride off to work and that makes a big difference on how refreshed you'll still be after you get there. I towel off, cool down, apply the "Old Spice" wipes and fresh cologne, and presto.........ready to face the world. I dont wear lycra either when I ride. Just regular shorts, sleeveless t-shirt, and my "Diadoras" with no socks (my preference).
If I have a problem on the road, break down, or just simply 'punk-out', I'll call my wife and order e-vac. No problem!!