I dson't know of any place where you could "lease" a shotgun or rifle for that matter. A matter of legalities, or rather, liability. You can buy a new Benelli Nova shotgun in Anchorage for just under $300.00 even as a non-resident and if someone did "lease" guns for a week, it probably would cost you that much. If you will be fishing amongst other people in close proximity, I don't recommend it, but that's just my 2 cents.
you can pick up a cheap pump gun for around $200 bucks that would do everything you need it to. A good head on your shouldersand being aware of your surroundings is much more bear protection than any shotgun could ever be.
All the rivers you just named are heavily fished during peak seasons and sometimes it is shoulder to shoulder. Trying to carry a scattergun while combat fishing would be a real pain in the butt. A big can of bear spray would be much easier to shove in a big pocket.
The fishable part of the Anchor River is very populated these days. You would have a better chance of having your scattergun stolen by the local teenagers than or ever seeing a bear around here.