There are some waterless wash techniques that some people use, especially in areas like Florida where there are water restriction zones. I haven't used this certain product, but I have used Citrus Wash and Gloss and love it, so this should be a good product too. I wouldn't trust any over the shelf waterless wash products, just stuff on like autogeek, detailedimage, chemical guys, or a few other low key but detailer trusted brands.
As far as polishing goes, you living in an apartment building I'm going to guess you'll be working in the sun. Try Poorboy's World Polishes, specifically the SSR 1 and the pre wax cleaners. They work very well in the sun unlike some polishes. Use 2, 2.5, and 3 for heavier scratches. You can work these in by hand without a buffer, it just takes longer. Are you sure you wouldn't be able to run an extension cord out?
The most important solution to keeping a clean car in such a restricting environment is PREVENTION. After cleaning your car, invest in a wheel glaze or sealant for your wheels, then you can basically wipe the dirt off with a clean cloth. Try DP Wheel Glaze, Wheel Wax, Poorboy's World Wheel Sealant, or any paint sealant will do (use very little for ease of removal). Regular waxing and touch ups with detail spray will remove and prevent a good amount of dirt from forming on your paint.
The waterless wash kind of scared me at first, but the lubricants encapsulate the dirt. It'll work fine unless your car is really dirty, then you should be careful. Use a bucket of warm water to rinse off the waterless wash applicator every few wipes to remove the dirt.
Let me know if you have any other questions.