I disagree with the other answers. I believe your best choice is a simple "cash out refinance" instead of a home equity loan. Here's why:

 1. Under the new tax law, interest paid on HELOCs is no longer tax deductible, and interest paid on the first $100K of a home equity loan is only tax deductible if the money is used for repairs or upgrades to your home, which doesn't apply in your case. With a cash out refinance all (or some) of your interest paid would be tax deductible (if you already itemize or if this enables you to itemize).
 2. With a cash out refinance, your interest rate will likely be lower than a home equity loan.

The biggest downside of the refi is you have to pay much higher closing costs than you would with the home equity loan (which sometimes have no fees at all). If you were only borrowing the money for a year or two, the extra fees may not be worth it, but you stated you're thinking about a 10-15 year term. In that case the lower interest rate and the ability to deduct the interest should easily tip the scales in favor of the refi.

Side Notes:

 - The above assumes your home equity is quite a bit more than $100K.
 - What you want to do really ought to be called a "cash out finance" instead of a "cash out **re**finance", but alas, no one calls it that.
 - Beating a dead horse here, but, with few exceptions, someone who amassed $100K in credit card debt is unlikely to pay you back in full in your lifetime. I got the impression you know this and are OK with it, and that's really nice of you.