Can you give baby an outie if you cut the umbilical cord for the mom?

It depends.: The appearance of the umbilicus (bellybutton) ultimately becoming an "outy" or an "inny" depends on how much of the stump remains on the baby after severing the cord, and how much of it survives. The more stump that is left and survives, the more likely it is to become an "outy".

Unrelated: The eventual appearance as an "innie","outie" or a stage in between I cal "poutie" has nothing to do with events at delivery. Docs can slice it close or leave a foot, it doesn't matter. The process of drying and stump separation that goes on over the next week or two contribute to the issue, as does the degree of weakness of the abdominal muscles.In the end, it will be as it would be.