I wouldn't give him anything wood. They will bite through it and break off little pieces at a time. Mine got into my wooden basket and went in my sons room and found pencils...they had pieces of wood in their poop

Also Timmy got sick on me and had to get some x-rays of his belly...when the vet showed me the pics he had something in his stomach and we couldn't tell what it was.....2 days later he pooped out pieces from my wooden basket. That is not good for them...it can actually do some damage. Mine used to chew on my walls and furniture..I bought bitter apple which worked great for us.
Try to buy him belly sticks or even a Kong....mine love them and they go at it for hours.