Brownells sells a tool to fix a dented barrel, but it is pricey. It would be cheaper to find someone who has the tool and pay them to use it.
I have what may be a similar gun (Cresent Arms, external hammer). I believe mine was made around 1930. The barrels are Damascus Steel and in good shape. I shoot it with light black powder loads only. It's still a lot of fun to shoot with light, pain-free, no-recoil, smoke belching loads.
I am not sure, but I think the chambers are only 2-5/8". I am going under that assumption and trimming cases accordingly, or using brass Magtec hulls (which are short enough).
If yours is anything like mine, don't be tempted to stick any store bought smokeless shells into it or it more than likely will not do well. If your barrel is Damascus steel that has been abused, have it checked over very carefully before you use it. It is best to have it checked over even if it appears mint.
I would not think a Damascus barrel would do well to have a dent removed, shortening it instead might be worth considering.
For what it's worth, you aren't holding an excessively high priced antique in your hand. Crescents (under various names) are really common. Sadly, you have to weight the cost of proper fixing verses what a better one could be bought for.