It sounds to me like you're loaning your cousin money.
Now, you ask about personal liability. What sort of liability are you asking about? Tax liability? You can gift him the interest, no problem, without any issues; so you loan him $14k today, and then gift him 5% interest forgiven each year, and he eventually pays you back, all square. (And if he never pays you back then some year you'll officially gift him the $14k, and write off the loan in your head.) The interest amount is well under the annual exemption for gift tax.
As far as I know, having a gift or a loan doesn't create any additional liability on your part (like, liability to pay his mortgage if he defaults, or liability for a slip and fall). If you're concerned though about legal (law) issues here, though, this isn't the place to ask those.
From a financial standpoint, there's nothing wrong with the arrangement you mention and it's very common. I would just note that you should personally consider it a gift, and just be happy if you eventually are repaid.
As far as the mortgage goes, it's up to your cousin to declare it or not, nothing on your side. Mortgage companies are pretty smart about that sort of thing, and one thing they'll want to look at are several bank statements - so a recent gift will look like a gift. Either way will be pretty similar in how they treat it - they'll raise the interest rate some or refuse to loan, if this is most or all of the down payment in particular. They can't be sure it's not a loan, so they treat it as if it were.
When it might come into relevance is if your cousin repays you then a month or two later defaults and declares bankruptcy or similar. The bank might then try to collect from you in that case, if it discovers the payment. I'm not a lawyer and don't have any idea of how successful they might be, but it's a possibility. Again, the fact that it's a loan doesn't matter there; it's just the evasion of his duty to pay the mortgage lender.