There is indeed a conversion factor: it is just the ratio of the
densities of the metals in question. For example, if you are talking
about pure metals, a piece made in copper will be heavier by a
factor of 10.5/8.96, or 1.1719 if made in pure silver while also
using identical volumes of the metals. When considering various
alloys, the situation gets more complicated, since the mixture of
metals in an alloy affects the density.
Luckily vendors of precious metal alloys often provide the ratios for
the purpose of estimating costs. What could be tricky is the fact
that a design that works in one metal may work better using
different size components in another design. (A stiffer, stronger
alloy just requires less material than the pure and soft metal.) That
means that the density ration of the pure metals is no longer a
simple factor in relation to the weight of the finished object. Of
course if the design is something like a struck medallion, strength
is not an issue.