Yes, you can use it on the wood floors. However, you need to be careful because the wetter your floor gets, the more damage that will be done. Has the urine actually seeped into the wood itself? If so, really the only thing you can do (that I'm aware of) is to sand down to where the wood is completely untouched and then refinish the floor.
Have you read the thread at the top of the forum on how to stop inappropriate urination? Click here
to read the thread.
Also, have you tried the enzymatic cleanser called Nok-Out? I (and many others) have found that it is the most effective one out there.