I see.
Something that would suit your application better and be easier to control would be a fiber coupled laser.
The laser is directed through a fiber optic which can be flexible and easier to hold than a large laser.
Also, 4W is a lot of power. In my opinion, too much for engraving wood. In the right circumstances you could end up getting a flame from the wood surface.
2W would be the most I would go with if doing it by hand.
Also, anything in this power range, especially fiber coupled, is going to be quite expensive.
If you haven't already, I would look into alternative methods for cost-effectiveness.