I think it needs a water gun. If the diaper was a spray on layered rubber, like a sponge then an impermeable layer, and then you sprayed a solvent to clear the old diaper and poop and then spray on a new one. You'd just need to slot them into styrups briefly or some socks on strings to move the legs into a good position.

But can this be done with baby skin and lung safe chemicals at a reasonable temperature?

Point being humanoid designs for robots that manipulate objects designed for humans are an artificially hard problem we have decided to fail at solving.