Having spent 3.5 years in Alaska in the early 60s, and took two Kodiak bears I would not even consider such a cartridge or rifle as the AK and 7.62x39. the two I took were with a .300 WBy which took several shots after the first 180 Nosler went through both shoulders, and a .375 which only required one shot.
My buddies used .35 Whelen and .300 Wbys. None of us ever had any problem but some did require follow up shots. While a 30-06 will do a fair job I know of at least one other friend who lost a Brown after shooting him with a 30-06.
I once was on orders to go back to Alaska and was going to take a .35 Whelan, and a 330/06.
It never made any sense to me, and still doesn't, that a person gets a chance of a lifetime to hunt big bear, and takes an under powered rifle. If I did not have a gun like a .338 I would buy one. The cost is miniscule compared to what a guide and licenses will cost.
I agree that there is not a guide in Alaska who would take a hunter armed with a 7.62x39. It might even be illegal, but I have not checked.
When I was there in the early 60s you could take a polar bear, either a brown or grizzly, and three blacks each year. I never hunted polar bears.
My advice is to get a proper rifle or skip the hunt.
Regards,
Jerry