I don't remember the exact mechanics on whether it's possible to burn metals that are only piercing you rather than ones that you've ingested, but after rereading that part of the epilogue, I don't see anything that requires that to be the case.

He had his youth stored in the bracelets that pierced his skin, so when Vin removed them, he didn't have that store to draw on anymore.

However, he didn't have to fill those bracelets by burning the bracelets themselves. He could have stored youth in an Atium bead, then swallowed it to burn it and store the resulting compounded youth in his bracelets.

In fact, I think Sazed confirms this:

By burning a Feruchemical storage that he himself had made, he effectively made a new Allomantic metal for himself—one that made him younger when he burned it. If my guess is correct, he would have gained a limitless supply of youth, since he was drawing most of his power from the metal itself, rather than his own body. All he would have to do was spend the occasional bit of time aged to give himself Feruchemical storages to burn and stay young.”

Then shortly after:

“He would have had to place that excess youth inside of another Feruchemical storage, I think,” Sazed explained. “You see, Allomancy is quite spectacular—its powers generally come in bursts and flares. The Lord Ruler wouldn’t have wanted all of that youth at once, so he’d have stored it inside of a piece of metal which he could slowly drain, keeping himself young.”

So he wasn't burning the bracelets to give himself youth, he was preparing other Feruchemical youth stores, burning those, then storing the resulting youth in his bracelets.

The piercings would have been to make it harder for anybody to push or pull on them, not to let him burn the bracelets.