In my own experience (I have worked a time with ichtyologists and marine biologists), the only way to fix a bit this problem of the decomposition of water organisms' matter, is a long bath in formalin, thus that's a way to avoid, definitively, because formalin is extremely hazardous. And even after this long bath in formalin, the organic matter keeps a bit of bad smell, as long as it can take some moisture inside. Then, there are no reasonable issues to fix that, especially in case of circle pearls smelling bad, because there's a high organic matter concentration in the back of their paths, which are always in local moisture.
Edit: maybe salt concentration makes the difference between circle pearls smelling bad or not, because salt catches more moisture. Thus, it might be interesting to bath pearls several times in pure waters to remove salt as far as possible, fist...?