Iridium has almost the same density as osmium (indistinguishable without precise instruments) and unlike osmium or rhenium it is neither toxic nor radioactive (even platinum is very slightly radioactive).
So iridium would be the safest among the densest metals for contact with human skin.
Unfortunately, not only iridium is very expensive, but it is extremely difficult to shape, being much harder and much less ductile than platinum (and its melting point is also much higher).
Platinum-iridium alloys are much easier to shape than pure iridium, but still much more difficult than pure platinum. In the second half of the 19th century, when new standard meters and kilograms were made for distribution in all countries and to replace the original standards made of pure platinum, an alloy of platinum with 10% iridium was chosen, as the most resistant metal to mechanical and chemical degradation that was known at that time but for which it was still possible to process it into a given size and shape.
So iridium would be the safest among the densest metals for contact with human skin.
Unfortunately, not only iridium is very expensive, but it is extremely difficult to shape, being much harder and much less ductile than platinum (and its melting point is also much higher).
Platinum-iridium alloys are much easier to shape than pure iridium, but still much more difficult than pure platinum. In the second half of the 19th century, when new standard meters and kilograms were made for distribution in all countries and to replace the original standards made of pure platinum, an alloy of platinum with 10% iridium was chosen, as the most resistant metal to mechanical and chemical degradation that was known at that time but for which it was still possible to process it into a given size and shape.