Here's a series of photos I took while re-cutting the nose of a Hawken hammer. The lock is a Davis, and the hammer underwent a lot of filing to make it presentable. But the first step was to recut the cup. I simply clamped the hammer by the flat part in my drill press vise and leveled the nose. The drill I used is a re-ground bit to create a slight taper which reinforces the bottom of the cup, and cuts a flat bottom. The spur of the hammer rests on the drill press table - lots of support. I simply positioned the bit over the cup, and drilled away. A light touch. When I worked for Don Robinson in the late 70's making our version of the Hawken rifle, I made up this bit, and drilled about 180 of these hammers.
This is a before shot...
...and an after shot...notice how much farther the hammer comes down over the nipple, and also moves forward so that the hammer strikes at the rear of the cup.
the recut cup...
And last, here's the re-ground drill bit. I flattened it first, and then cut some draft on the cutting surfaces. Then I ground the taper into the bit, again providing some draft so the bit would cut rather than squeal and heat up.