Many people use a new model of the old push mowers (AKA reel mowers)
Many people use a plug-in (or probably by now rechargable) mower
I have heard of a solar powered robotic mower (related to the roomba vacuum) but I don't know if those are still made or if they never worked out.
A fourth choice, if it is available, might be to see if other people in the townhouses have a contract with a lawn-care professional (or neighborhood kid)
I had a similar dilemma for my home, but the grass was now in a normal square plot shape but decorative with other stone paths.
I used a weed wacker at first but always kicked up the stones, then I went to manual trimmers and it actually didn't take that long.
Note- I also lived in a dry, sunny climate which didn't need grass cutting weekly.
Quicker than scissors, easier to store than a mower. Also consider replanting a moss or other non-grass green area that wouldn't require mowing. (When you think about it, it's pretty wierd that we favor the one type of plant that has to be topped every couple of weeks to not be overgrown.)
Establish Centipede or Zoysia grass. Neither require cutting if you don't mind 6 inch tall grass.
We have a postage stamp yard. Our front yard is mostly driveway and gardens. Our side yards are about 15 feet wide. Our back yard is about 75x25.
At first we just bought a push mower. But we're in the south and our grass is Bermuda grass, which is very tough, so that didn't work out too well. It might work for you, though, if you have a finer grass like perennial rye or Bluegrass.
So we ended up getting an electric mower and it works fine. We just couldn't see dealing with the noise, pollution, and gas can for a gas-powered one for this tiny amount of grass. The funny thing is we have neighbors with lots no larger than ours riding around on riding mowers. That makes no sense at all!
Some stores sell the old fashioned push mowers which would be a good choice for a very small patch of grass.
usually just use a weed whacker.