how is the cupboard located. is it flush into the wall etc. you could possbily cut a whole at the top and bottom, and glue/screw subtle vents/grills over them, and then have an intake fan attatched via duct tot he bottom and an exhaust at the top along with a carbon filter. although if the doors are sliding it could need to get more creative.
while leaving the doors ajar might be fine in terns of fresh air etc, you don't ever want to set your grow up in a manner that might compromise your safety, or the plants health, should an event arise. you want to be able to have someone walk into your room and you not have to move but know that your grow is safe unless they start opening doors etc.