Can't get son to drink

My son will be 15 months this week and is still nursing 2-3 times a day. I can get him to drink a bit of water from a sippy cup, but he refuses to drink anything else. He'll take small sips of almond or cow milk from an actual cup, but that's it. He's begun self weaning and I'm worried he's not getting enough fluids. I try to offer drinks constantly through the day, but the only thing he'll drink more than a sip of is water. What should I do? I don't want him to become dehydrated or miss out on nutrients when he completely weans. I've actually kind of been pressing him to continue nursing just to make sure he's drinking enough fluid. (We just moved to another state and haven't switched insurance yet and I don't have a new pediatrician here for him yet, so I haven't been able to take him.)