NO DO NOT PUT THE WRAP ON IT.
Your paint needs to cure. Regardless of curing or not. there is a possibility even on fully cured paint that if you put film on and them REMOVE IT, you RISK the possibility of LIFTING YOUR PAINT.

I would either just drive it with painters tape..... or just drive it without.
Are you planning to to not drive it when you get back home since the car is all nice and shiney and fresh..

It's just a car...either rent something you would feel comfortable with on the road or just drive it....