I always changed the diaper anytime it needed it even just for pee. I never wanted to take even a small risk of the baby getting a rash.
BTW - have you tried to give a bottle at 1 am? The baby might sleep all the way until morning and skip the 4 am feeding if they get their bottle at 1 am. I never stuck to a "schedule" for night time. If the baby woke up, even if it was earlier than normal, I would often give a bottle to see if they wanted it. In most cases, once a night was all they would wake up, but it wasn't always the same time.
One trick I found during the night was to learn to do everything with the least amount of light possible. I had some well placed night lights around the baby's room that gave me enough light to see what I was doing without turning on an actual light to take care of middle of the night feedings and changes. Too much light can stimulate a baby or a toddler and they end up awake but still cranky because they didn't have enough sleep yet. I also avoided any form of stimulation for the baby during the night. I said as little as possible.....just enough to comfort the baby if she was fussy. Basically, keep everything calm and as dark as possible, do what needs done, comfort the baby, and leave the room. The lack of light and stimulation will keep them calm and they should go back to sleep.