I am not really able to say anything about polar bear hunters specifically, but I wrote an answer to a similar question a while back.

In general, the further away from a major river and the further north this polar bear hunter lived, the less likely they would be to know of any Russian presence, but even for people who had no personal contact with Russians, either their epidemiological environment or pastoralist land use patterns would be greatly disrupted and they would eventually hear from some acquaintance somehow. The effects of Russian colonization were very wide-ranging, and not just limited to imposing an administrative regime.

On the other hand, even as this polar bear hunter will almost certainly learn that Russia now "controls" Siberia, the extent of that control could be very limited. Siberian peoples proved rather difficult to incorporate into Russian administrative structures, both because they were unwilling to give up their own ways of life, and because they would quite often try to make it difficult.

However, I'm beginning to run the risk of rewriting the entire answer, but with fewer specifics and less thought put in this time, so I'll stop there and recommend you go read the link. If you have any follow-up questions, I can also try to reply them if I know the answer. I also included links to some other high-quality answers by other users on similar issues related to the colonization of Siberia, and the answer to a follow-up might be in there.