I don't think you need to worry about hunters. When I have been driving on rural roads there are clear signs when they are hunting. But I guess it could be an issue if they start the hunting when you have already been in the woods for some time.

One way to minimize the risk is to contact the owners of the land where you plan to stay and ask who is hunting in the area and then you can contact the hunters. You can find the different jaktlag (hunting party) here https://jagareforbundet.se/var-verksamhet/lansforeningar-och-kretsar/ you can select the region under "Kretsar" and you will get the different jaktlag in that region.

Or you can ask in the local hunting store if they have one in a town close to where you are staying.

Are you planning on hiking or driving around? If you stick to the many and known hiking trails then I wouldn't worry about it. These are definitely known by the hunters in the area. Also wear something bright and colorful to increase your visibility. A hat, scarf or rain cover for your backpack can help a lot.

I would stay out of the woods during the first weeks of the moose hunt. I think it starts in the beginning of September in northen Sweden and beginning of October in southern. But maybe someone else can verify that?