Anything helps, of course. Anything is so much better than nothing.

You are skinnyfat, yes? You don’t want to lose weight, you want to add lean mass. Weights are what do that best. Ideally you would want to lift heavy at least thrice a week if you are trying to shape up.

I can only lift once a week lately (lady, mid 50s) but do yoga 4x/week too. It’s maintaining me reasonably lean.

I have been where you are (single working parent) and what I did back then was wake up at 5am and run, because that was the only time of day nobody needed anything from me, and running is nearly free, just shoes. It sucked, but the days I ran I did feel better later on, it was worth it overall I think. If there is any way you can wake up a half hour earlier and do something vigorous, and then add weight training once a week I think you will get good improvement. Just maybe not as much mass as you ideally want.