Yes Fabuloso cleaner is a great cleaner for mopping wood floors with.
I use the cleaner Fabuloso all the time to mop my wood floors and it does a great job at cleaning the wood floors.
You can also use Vinegar and water to naturally clean your wood floors but just avoid getting the wood floors too wet so that you don't cause warping of the wood floors or cracking the wood floors.
Make sure to dry out the wood floor after mopping it to avoid damaging the floor but using Fabuloso or vinegar and water will get the wood floors clean and won't harm the wood floors.