Although it is far harder to obtain a refinance with a Loan to Value (LTV) of 100% than it was a few years ago, it still may be possible.
I did a quick search online and found several companies offering 100% financing. The companies, alas, are not household names in the refinance business. I do not know the fees they charge nor their reputations, so I suggest that you shop around. It is my opinion that this will be a difficult loan to source.
When you are seeking a loan that is 100% of the value of your property, any loan you are likely to find will have a higher interest rate than a loan you could obtain if you were in a strong equity position.
You may have heard about the HAMP program. The Home Affordable Refinance Program is available to residents of their homes whose first mortgage is no more than 125 percent of the property's current market value. It is open to open to homeowners whose mortgage is guaranteed by Fannie Mae or Freddie Mac. Borrowers must be current on their mortgage, but at risk for foreclosure. To qualify a homeowner must also not owe more than $729,750 on a single-unit home, and their monthly mortgage payment must come to more than 31 percent of their gross income. Because you are not at risk of foreclosure, HAMP is not the right program for you.
You mentioned that may be able to bring some money to the table to close the loan, though you would like to make your cash contribution as minimal as possible. Bring cash to close the loan is a good idea, especially if you can bring at least 5% of the loan value. I think that you will find more lenders willing to offer you a 95% LTV loan than a loan for 100% LTV.
You stated desire to obtain a 15 year loan. To me, this means that you are able to make a higher payment than you are required to make on your current loans. If that is the case and you are not able to obtain a 100% loan that meets your needs, it may make sense to simply accelerate the repayment of your current loans. If so, it makes sense to increase the payments on the loan that is adjustable, which your HELOC likely is.
Without knowing more about your income, exactly how much you can afford to bring to the loan in cash, and what other assets you may have, it is hard to advise you as to your best option. For instance, it may make sense to borrow money from a 401K plan, if you have one, to improve your LTV, depending on what interest rate you will pay on the 401K loan.
Lastly, I suggest that you look into FHA loans. FHA loans can often go out to over 97% of your home's value. It may not be 100% financing, but it is close.
I hope this information helps you Find. Learn & Save.