normal pla is actually easier and better to use for colouring.
xyz make a printer that uses neutral colour pla and colours it with an inkjet printer head for full colour prints.
https://www.xyzprinting.com/en-GB/pr...da-vinci-color

Wood filament tends not to take ink that well as the wood absorbs the ink and wicks it away from the surface.
I'm basing that on trying to use standard wood colouring stains.
It just doesn't stay on the surface of the prints and looks blotchy and awful.

So you'd be better off using neutral pla and colouring it so it looked like wood.