Beardies get most of their moisture from food. Things like collard greens and squash have high water content and you can give them a quick rinse before feeding. Even crickets have a good deal of water in them. So you may have nothing to worry about. You say he's not eating his veggies; is he eating at all?
Wrinkly skin is normal to an extent. They have excess so they can twist and turn their bodies, or it could be related to shedding or slight weight loss. A way to test dehydration is to gently pinch a bit of skin and hold it for a few seconds then release. If the skin went back into place quickly he's getting enough moisture; if it stays raised for more than a few seconds and is slow to move, increase water intake. Another thing to pay attention to is his stool. Is it hard or soft?
I would try (if you haven't already) just dribbling a bit of water on the snout during
bath time. Be careful not to get water in the nostrils. By just letting the water drip off your hand onto the nose, your beardie should stick his tongue out to check it out. Even if he doesn't, water still gets soaked up through the vent during baths.
