If it were me, I might do both methods, one as a rough-in and one as a finish pass. The first would be to roll the cone in the swage over the mandrel. No slot needed in the mandrel - you simply heat the steel and sink it then wrap the edges with the hammer around the mandrel (while still in the swage). Next, reheat that blank, drop it in the form and drive the mandrel in to finish the shape.
We also should consider the math on the material. If you use a 1" handle, you'll need 3.1416" of material to encircle it. Of course, that is more precise than needed so 3-1/4" wide will work. You could either cut this from sheet metal or flatten it from bar stock. Theoretically, 1/2" round will get you pretty close to do this. Here is the math:
3.25"x1/16" = .205
Vol of 1/2 rd = .196
This only leaves you .009 short but the forging won't be a perfect 1/16 thick all the way across. Using 1/2 round tool steel would allow you to make the chisel and socket from one piece without welding, which is usually good practice. It would also give you enough material on the working end to make most normal chisel sizes.
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