Contact out of the blue; the postdoc will be proud to have been noticed. But remember that postdocs are in the tightest bottleneck of their lives, having to produce research of high quality quickly in order to get the next job right now. If the postdoc does not see how to get a paper out of your idea immediately, the postdoc should reject the opportunity for collaboration withwithout wasting your time or hers. Do not be offended; starting a research collaboration with a new collaborator can take a lot of time, just to learn how to work together, even if both are very experienced in their fields. Many very top notch researchers have been rejected when they have asked to collaborate with even far less reknowned researchers who were too busy.
You will need to have a collaborator within the academic world, to make certain that your results are not already known, and to get access to academic journals. Obtaining that collaborator is the only problem you have to face before you can really join the international mathematical conversation.