Yes, any kind of mop will work.

Or, Get something like a Sh-Mop with a microfiber bonnet. Wet the bonnet with water, wring out, place it on the mop and wipe the floor. Or a moistened regular size microfiber cloth on the end of a (dry) Swiffer.

Here is a link that might be useful: Sh-mop

Bona is great, and Swiffer makes a wood floor cleaner (but it's expensive). Suggest you sweep daily and mop as needed, maybe once or twice a wqeek. Good luck.

If I have wet paw tracks, I don't use water or a wet swiffer on my nice wood floors. I put a little Bona or even those pop up furniture wipes to clean up the doggie foot prints.
Linda C