For signing metal prints, the community recommendations point to permanent, acid-free markers or paint pens.

Most specifically, Bic Mark-it was recommended, including by Bay Photo after testing on their metal prints, saying it works well and does not rub off. A Pilot acid-free paint pen was also suggested.

If you prefer Sharpie, avoid standard versions that contain acid. Sharpie does make some acid-free, archival-quality models, and those would be the safer choice.

In short: use an acid-free, archival permanent marker or paint pen, with Bic Mark-it being the strongest recommendation from the answers provided. If possible, test the pen first on a sample or an inconspicuous edge to confirm the look and adhesion on your specific print finish.