Help: Can I clean my Sterling AX40D maple fretboard with #0000 steel wool?

I have a Sterling AX40D guitar with a dirty maple fretboard. I tried cleaning it with Ernie Ball Wonder Wipes, but it didn’t get the dirt off.

Questions:
1. It is safe to clean my AX40D maple fretboard with #0000 super fine steel wool?
2. If so, should rub with or against the grain?

Thanks for your help!