There is no such thing as lifting pedalling force under normal circumstances. This was proved years ago using strain gauges in pedals. The only measurable power advantage of clipless (compared to other pedals that let a rider apply power in the horizontal part of the stroke like BMX pin pedals) lies in standing sprints by athletic riders, where they can deliver around 5-10% more power and let a rider get up to max power output much more quickly.

1st things 1st, WAR EAGLE!

I used to pedal up US29 (not the best road for riding) from the outskirts of Tuskegee to my office on campus a few days a week.
Either dropped some clothes there the day before, or hauled my stuff in my Timbuk bag.
Had no shower, so it was always a sink basin cleanup, followed up with WetWipes & deodorant.
I made sure to arrive well ahead of time, as I have a bit of a blubber layer it takes me a while to cool down.
SPDs, always....shoes were kept in my office.

Even at 6:30am, AL is nasty hot & humid.

Skip the shower, sink washup and change of clothes for a few weeks and they might suddenly change their minds.


As for me, I don't think I could commute without shower access, which is why I love commuting to school. Well, MAYBE in the winter I could pull it off. Yesterday, before the storm blew in, it was about 90 degrees or more with about 50% humidity. I walked from my place to my uhaul storage directly across the street and back, probably less than 5 or so minutes, and once I got inside, I had to change shirts! I sweat. A lot.

So for the OP, you just have to try it out a few days to see how it goes and tweak your plan along the way. Along with baby wipes, your can also check out shower wipes made for camping. They might be more expensive, but they're made to specifically handle the job in question.