The problem with a jeweler's ring mandrel is that with the taper, it may or even probably would flare the muzzle while you do the work and before you got most of the dent out.
There are two ways to fix this, the most common has always been to saw off the barrels behind the dent and then “true up” the muzzles of both barrels. Normally you won’t loose much of the choke in each barrel that way and it is the most cost effective way to do it.
I have never "ironed out" a dent in a barrel, as the work is called, but studied how it was done when I had to iron out a dent in a pump shotgun magazine tube.
First, did you ever accurately measure the inside diameter of that barrel and record the measurement? It is not a requirement, but it sure would be helpful. You cannot just go off the measurement in the other barrel as sometimes (to normally/usually) doubles are choked tighter in the "second" or other barrel than the barrel that is fired first. Now if you know the barrel that is not damaged is indeed the tighter choked one, then one begins with that measurement.
So if you do not want to saw the barrels off, do you know if the dented barrel is the tighter or looser barrel? Also, did you ever have the barrels “jugged choked” after they left the factory?
Gus