Equity vs. Credit Card Debt

I have a mortgage balance left of only $18k at 5.75%. Problem is I really need to get some cash equity out of this house to eliminate 30-40K of credit card debt.
My fiancee, (now wife) has worked for my company receiving annual 1099’s for around 30-35k with little to no debt. Both of our names are on the deed to this property. Is it possible to do a cash out refi in one or both of our names? Or prehaps a debt consolidation loan or HELOC?
The first thing in the continual tightening of the guidelines is for self-employed individuals. Lenders and underwriters are required to calculate two full years of tax returns and profit and loss statements. We use the adjusted gross income, but can add back in depreciation. Also, on a cash out refinance, you will pay a premium to the interest rate and/or points if your credit score is under 720. We would be happy to evaluate your loan if contact our office as our job is to say yes on every loan. With the current lending environment, a lender almost needs to take a blood sample in addition to receiving all of your documentation.