Should we hire a nanny as an independent contractor, will this still allow us to claim the child care tax credit?

[Critter-3]

Either you have a household employee  or you do not ... you do not have a choice on how you handle this. 

https://www.irs.gov/businesses/small-businesses-self-employed/hiring-household-employees

[Opus 17]

You can claim the child care credit if you pay for someone to care for your child or other dependent under age 13, so you (and your spouse if married) can work or attend school full time.  You must include the care provider's tax number or social security number on your tax return.

How you employ them does not matter for the credit, but it can matter for other reasons.  A worker is an employee or contractor based on your working relationship.

https://www.irs.gov/businesses/small-businesses-self-employed/independent-contractor-self-employed-o...

If you hire someone as a contractor, but your working relationship is more appropriate for an employee, and they complain, you can face significant federal and state penalties.