Applying for new credit cards shortly before renting at a new apartment?

So, I recently applied for a Chase Freedom Unlimited for the 0apr period and to have a catch all card, i want to also apply for the CSP, that being said I am looking at moving and applying for a new apartment lease. How would 2 new hard pulls about a month before the lease application affect the application? I can delay the CSP application but I would like to use it for all the transit (gas, tolls, etc) for the drive (about a 20 hour drive) and then obviously later on after the move, flights and hotels.