Air drying is certainly better for stability, but if you’re in a rush you can try to pop it in your oven for an hour or so at a reasonable temperature and hope for a decent result — times will vary based on the thickness of the material, etc, and there may be an increased risk of splitting or who knows what else. At about 6:27 in this video, a former student of Paul Sellers, Andy Rawls, who is now a fine woodworker in his own right, oven dries a small piece of his Christmas tree for use in making an ornament for next year’s tree: https://youtu.be/gQKsGjE9X3M?t=6m27s
As for the issue raised by btyreman, maybe think about it this way. You’ve spent many hours improving your craftsmanship. You fret over tight joints, flat faces, 90 degree edges, smoothed show surfaces, interesting visual details and grain patters. Why? Because you want to maximize the pleasure when interacting with your products.
So perhaps the choice of allergenic woods and CA glues for a food prep surface can be looked at in the same light. Sure, it’s a small chance that someone will get an upset tummy from freshly-cut veggies, but by the above standard it represents a lapse in craftsmanship — you’d have moved backwards and decreased the pleasure from interacting with your products.
Of course if this cutting board is, in surfer terminology, a “wall hanger” — not to be used except for show — then that’s a non-issue. Be sure and post photos of the end result!