The Death God's hand catching Orochimaru's soul was ok, but how would it catch the soul of a demon. Spoiler from the manga:
So this means that most likely the demon's soul was not just pulled out like the 3rd hokage did it with those 3 souls.
The 4th could have a kage bunshin to hold the baby while he fights the demon fox, so there are various combinations he could have used.