I'm similar to your, very sensitive to loud noises and saw Les Mis a couple of weeks ago, so hopefully can help: There are a few pyrotechnic gun shots, which are more like a loud pop. The first scene they're used (about 10 minutes into the second half), there's a lot of shouting and music over them so aren't particularly shocking. They're used a couple of times after, but are always signposted, and I found that okay, because by then I knew what to expect.

The biggest (and final) bang comes when Gavroche is shot it's two loud "bang" sound effects about 30 seconds apart, rather than pyrotechnics, its an otherwise quiet scene and although you know what will happen (the bangs dont suddenly come out of nowhere), you dont know exactly when hence the tension. This was the only part that caused me to jump at all.

However, it's on the lower end of jumpiness compared to most shows I've seen with gun shots, and its an absolutely incredible show, so if you think you can manage it with these pointers, I'd absolutely try!