You'll need to be very careful since you cannot obtain the same
angles on the crown as when it was originally cut (if cut with a
regular machine that is). I would use something like Alumina B mixed
with a little water. It's .03 micron so if you have problems it
should cause minimal movement of meetpoints. One caveat is that it
will polish slower than Cerium which could cause scratches and is
more aggressive (ie may move facets).
Is it more a 'cab' or a faceted stone? The scratches are definately
not stress fractures, etc right? Last thing you want is to start
tearing off pieces of the stone trying to polish out a crack :).
Also, use a slow speed you don't need to go fast it'll just cause