I used to commute 6 miles each way, often didn't shower at work even though there was one. really depends on how sweaty you get/how hard you cycle. as others have said, wet wipes, small towel & sink, deoderant, and clean fresh smelling clothes. I'd often shower at home before cycling so I'd only really need to have a sink wash to freshen up.
if you don't have dry bags (alpkit gourdons are great) get one so yr clothes stay dry. I used to take a weeks worth of clothes in on Monday to avoid having to carry much the rest of the week. sometimes takes a bit of planning - you will undoubtably have a day when you arrive at work and have forgotten socks/underwear/shirt etc so just plan and know where yr nearest clothes shop is!!!