In my family, we routinely made loans to one another, often because someone had money tied up in bonds or CDs and wanted to borrow for a house, etc. Like your situation, the lender would get a better than market rate and the borrower would get a better than market rate, and you have none of the closing costs associated with getting a regular loan. It’s truly a win-win deal.
That being said, you have to really know and trust each other. It sounds like you’re pretty safe, and I really don’t see why you shouldn’t do it. Just remind this relative that interest rates could go up, and they would miss out on those better rates, IF they go up. Make sure they know that they can’t call the loan early (unless you want them to), and that they will be stuck with the low rate you’ve agreed upon. Make sure they really understand this and that they agree not to get upset or try to pressure you to pay off the loan early in the event that rates rise of if they decide they need this money for some reason.
Just draw up a legal contract, and have them record the note. There really shouldn’t be too much extra paperwork (we didn’t have too much). Make sure you check with a CPA to be sure everything’s taken care of, and maybe have a RE atty take a look at your documents.