If the dents are at all visible in the bore, I would want to raise them before shooting, especially in Damascus barrels.
In any event, I'd prefer to raise them just for appearance sake. And raising common dents in the thinner portion of barrels is one of the easiest DIY gun repair jobs there is. It does become harder when a dent is closer to the breech where the walls are thicker, but those areas are much more resistant to getting dents in the first place. And of course, a sharp dent or one where metal is displaced is more critical. If it is deemed repairable, it will often involve striking the surface and refinishing. Polishing on the inside may be done too. This can leave a thin spot in the barrel wall that could rupture if too much metal is removed.
I believe you said you are a machinist Jholland. If so, you may have access to a set of plug gauges. You slide in the largest one that will fit snugly, centered under the dent, and begin lightly tapping all around the dent with a small hammer. I use either a hard plastic faced hammer or a small brass hammer to avoid marring the barrel. Very thin tape or plastic film can be used to avoid leaving marks, especially from a brass hammer.
Tap all around the dent until the plug gauge becomes loose, and then insert the next larger size that fits snugly under the dent. Lather, rinse, and repeat until the dent is fully raised and a bore size plug gauge slides through to the choke. Done carefully, refinishing or touch up bluing is seldom needed. And it rarely takes me more than 15 minutes to raise the average dent. Hardly worth risking loss or shipping damage sending most barrels out to a specialist.
Lacking plug guages, you could also turn several on a lathe. Of course, the leading edge should be chamfered. Or even take the time to make a tapered wedge type dent raising tool, if you contemplated removing a number of dents over time.
I don't know if the anvil of your 12 ga. Brownell's hydraulic dent raising tool has enough stroke to be used in a 10 ga. or if it would work well. But the process of using a small hammer to actually do the dent raising is the same. They are not used like a hydraulic jack to push out the dent from inside. You could also do a Search here to read old threads on the process.
