No credit card required
Browse credit cards from a variety of issuers to see if there's a better card for you.
From what you've said it sounds like an FHA 203k loan would work, since it sounds like it's more than $35k of work it'd have to be under the full 203k program (vs. the streamline 203k program).
http://www.hud.gov/offices/hsg/sfh/203k/203kabou.cfm
The 203k will work there is a ton of work to do to get this loan and it takes a lot of extra effort. Not to discourage you but dont go in with blinders on either.
The 203k streamline is a lot easier and if you could get the costs to less than 35k to get it done you would cut the extra work down considerably (for qualifying)
Good Luck
Brian