I live near there, just north and east of Coffman Cove, on Wrangell Island. I go to Coffman Cove sometimes in my boat. I think black bear hunting here or there is similar.
Like the pictures posted already show, a boat is usually involved. In the spring when I have hunted bears, it is a matter of cruising around looking for them on shore, eating new shoots of grass. Then go to shore downwind and out of sight of the bear, and stalk on him. If you can pick out something next to the bear to keep in sight, like a big tree, then orient yourself when ashore, it can be pretty simple. A kill is often close to the boat, which is nice for getting it out.
Spring hunts can be good if you get a bear before it has rubbed a lot. If you want the meat, it is leaner and less fishy which is a plus. I used to make sausage from black bears, but have not done so for several years now.
The tides here from high to low can be over 20ft, so when you leave a boat on shore and go bear hunting, you have to know that, or when you come back, your boat may be aground for the next several hours, or it may have floated off. Best is if someone can drop you ashore and then mind the boat, maybe go offshore a bit and wait (go fishing). If you want a gun backup, that may mean a third person. If the tide is coming in, you may be able to tie the boat off and let it bump the beach for a while if it is not a rough ocean day. Somebody in the party needs to understand a tidebook.
You have to balance the need for a light weight shore boat with the need to get out in big water in Clarence Strait outside of Coffman Cove. Many tow a skiff with motor, behind a bigger boat to have both.
The other alternative on POW is the road system, which is extensive. There are over 1000 miles on POW, some of which is very nicely paved and some of which is rock and potholes. You can get to POW with a vehicle from Ketchkan via the Interisland Ferry, which goes to Hollis, and then you drive up to Coffman. They have cancelled (for now) the northern route from Coffman to Wrangell unfortunately. The forest service in Ketchikan can sell you a good road map, or you can get it on POW from the Forest Service there. You can access a lot of shore with the road with a little effort, as the roads are usually near the beach, but they do vary. A GPS with the map would be useful.
If you go very far into the dense brush here, consider having some colored flagging tape to mark your route out. It is not hard to get lost when you can't see very far. It is also helpful to mark a trail if you are packing something out and want to return right to it for multiple loads.
There are extensive cave formations on POW, some of which are still being explored. The entry pits to some involve a free descent of 100ft. or more and have been found to contain bones of fallen animals. Watch where you step in the brush.
As to the locals not liking bear hunters, there is a potential for a problem. However, I think traditional archers can easily show the respect for the animals and communities that common sense indicates. The problem is that the locals can sometimes identify more with the bears who live here than the hunters who come and go, but some sensitivity to the issues goes a long way. In these small towns everybody knows everybody else, so you will not go unnoticed, but being courteous and respectful does not go unnoticed either. I think we on TradGang know this by and large, but realize the locals have had their share of arrogant others to deal with, who leave with boxes of meat and fish. If you aren't a guide or a lodge owner, you may not see where it has helped you any, and that there is that much less in the woods and ocean for you to catch. I think there is room for outside hunters, and it is a part of the economy, but it helps if you appreciate the other side of it too, and try to acknowledge that you are in a special place having special experience. Give it some thought and you will be OK.
Hope that helps. PM me if I can help.
Walt