The birds need water frequently including when they first start moving, if you are up crack of dawn to provide fresh water removal is perhaps an option?
Logic suggests that water dispensed through nipples will not create much humidity. The greatest source of humidity in a coop would be their waste overnight and their breathing (I am not an expert so could be wrong).
I do know that eliminating humidity through appropriate ventilation is required. I would focus on achieving that and keep water in the coop 24/7. I both feed and water my flock inside the coop (hanging feeders/waterers with nipples). I built it to be predator/pest proof (and so far have not had any issues). I have a Woods fresh air coop and have zero humidity buildup in the winters.