I'm thinking that if you have backpacked for a while then, maybe you are familiar with "Bear bells", like sleigh bells, attached to your backpack, belt or boots, and or with "bear spray". I'd think upper NY state black bears are skiddish of humans, and I'd be of least concern. However, if you have a 9MM that "blast and noise" might just scare off 99.9% of black bears. Black bears are very fearful of noise. Myself I would not worry about it if you have bells, spay and 9mm. If you have a dog with you, put on the bells on the collar.

If you want to go to the extent of suiting up for a highly remote possibility of a black bear attack, then go with something no less than 41 magnum. This is a remote chance i'd think. I've encountered black bears and cats in the woods and all just turn tail and run off asap. I have shot one in Idaho. Bear bells on my dogs scare off bears and cats into the next county. I would not worry about this given the low cost options and your hiking area.

If you were in Wyoming, Montana, or SE Alaska, that would be a different story. In general, I'd be much more concerned about 2 footed animals.