If possible keep some clothes at work so you don't always have to be packing a full set. A damp wash cloth with a little soap is sufficient for a quick cleanup before changing into the work clothes.
BTW, make sure that there might not be a shower in the building. Places where I've worked all had showers, but in two of them no one else seemed to be aware of their existence. In both cases they were around for the maintenance staff in case they had to use some toxic cleaning products and wanted to clean up thoroughly. One shower was down in the basement hidden behind all the building power and HVAC equipment and the other was in one of the downstairs bathrooms behind a closed (but unlocked) door marked "MTCE." No one had a problem with my (or other cycling commuters) using the showers - but they weren't at all obvious or advertised.