I think your odds are better if you put in for an deer/elk combo. If you are coming in Sept then good gosh man,better have an elk tag in your hand, they'll be bugling.
You can carry a pistol while hunting. I carry pistol and bear spray. I wouldn't say there aren't griz and they are not to be thought about, as there was a man killed by one while he was gutting his elk on the Clearwater Game Range about 3 years ago.
I wouldn't let it freak you out, you probably won't see one, but you can't be stupid about food and camping and such.
The Swan Mountains are some of the most rugged and beautiful places you will find to hunt. If you are willing to walk at all you won't see people. Lots of big whities, Sept will be to early to catch them rutting. But that first week of archery is a good time to get one as they are still in their summer patterns of feeding in the same fields in bachelor groups of 5-10 deer. Get a treestand in a good spot next to a private hayfield and you stand a good chance. You don't stand a good chance stalking due to the brush and the randomness of the deer in the big woods here. My opinion of course. But seriously, put in for the elk tag and get into some of those basins in the Swan and you will have some fun. There is a good bull in every basin. But you better be prepared for some steep and deep and brushy hell holes, but that is nw MT. Some get in shape or you might drop a nut hunting this stuff, that's is you go after elk. The whitetails are in the rolling foothills and lowlands and creek bottoms.