I have padding under the carpet which all lies on concrete and they can easily sway side to side but not so much front to back. I tried setting them on some thin flagstone and some butcher blocks which made them more stable but the sound didn't improve any. The function of isolation is really what counts. I've been to audio salons and saw the same results with metal stands on solid wood floors but having no kids or pets makes it easy not to worry. I might even add some small spikes but don't really see the need: they stay put and sound great.
Aside from the incredibly inert nature of the maple wood and it's ability to isolate, I have to give credit to Herbie's Square Fat Dots which act as footers between the speaker bottom and the top of the stands. They are denser than the Tenderfeet and don't easily compress, if at all.
As for your wood floors, I'd opt for some small, thin area carpets under the stands and that should solve any problems. If you still have any doubts, keep in mind my speakers are only 8" wide so the stands are narrower than usual. As long as you keep the front to back measurement even with your speakers, you can go a little wider on the width and not affect the sound at all and it would still look nice.
All the best,