Question about Bissell CrossWave Pet Pro

I have done it with wood soap - works well.

Oiled by a professional or oiled for 100 years, then it should not be a problem with the right agent (as Urs has already mentioned). I would be cautious about DIY by hand with a cloth. The part is extremely powerful! One spot not 100% tight and there are clouds. But that has nothing to do with the device.
Maybe use the carpet mode at the beginning until you have confidence.

I use it on oiled floors it is perfect it is important to use the right product a floor soap that is not greasy then the floor stays beautiful I use rubio monocat floor soap it also saturates the floor