One of the print shops in town like Fast Signs or Alpha graphics cuts stencils.
Not sure if there is a difference with doing wood versus metal. I have seen the lasers burn graphics in. I don't recall one seeing wood sandblasted.
For gifts, My wife makes stencils using vinyl and her Cricut machine. She puts them on the Kodi powder coated tumblers. And I blast them in a cheap blasting cabinet. It creates a negative space in the powder coating and looks good.
The vinyl holds up to the blasting but I don't stay in one spot. The gun is always moving.
The vinyl sheets stick very well to the tumblers and don't peel up around the edges. That would be my concern with a wooden cutting board. Do you have a piece of scrap to test on?
I would imagine the print shops would know what sticks and what materials peel up. If you are running out of luck I could make you a basic test stencil to try on a piece of scrap. I don't have my blast cabinet anymore.
With wood I would be worried about edges lifting up, especially if there are really fine lines.