Nick, I think your idea of using a pipe cutter, which reduces the diameter of the pipe at the position of the cut, is a very practical one. I have made cell cutting punches from very thin walled stainless steel tube, and had cut this to the required length with a 1mm thick cut-off wheel in an angle-grinder.
Finding the best tubing to use, or even determining what type of material is best, may not be as easy as you would like. Stainless steel tubing can be sharpened to produce a keen cutting edge, but may not be easily found. Copper tubing on the other hand is much more easily located, but much softer. With copper tube it would be easy to make a cutting edge, and even if a sharp cutting edge was achieved it would be easily damaged because copper is so soft. Brass, on the other hand, is harder than copper, and if it can be cut and burred effectively with a pipe cutter could be a good choice. The cutting edge which could be produced on a brass tube would be more robust than on a copper tube, but not as durable as on stainless steel.
I was fortunate that I had some stainless steel tubing, of about 9mm diameter, which has proved ideal. In its "previous life" it had formed the horizontal rails of a light-weight (and not very robust) clothes airing rack that was of Chinese manufacture. Perhaps we should all be on the lookout for light-weight stainless-steel clothes airing racks, which we can repurpose!
While talking about the cell cutting punches which I have made, I would like to refer to Nick's comment, "As far as I can make out, the diameter reduction is so that the punched wax doesn’t fall out". This observation is correct. I did not have the use of a pipe cutter, and I do not know whether such a cutter could be successfully used on such thin walled stainless steel tube as I had. When a candidate cell is identified for queen raising, and cut from the comb, it must be gently pushed through the tube so that the harvested larva is accessible to the nurse bees. I was successful in burring over the non-cutting end of the cell cutting punches, and have found that harvested cells do not fall out after they have been pushed through the tube.
Various methods could be used to hold the cell cutting punches onto the cell-raising bar. I have fabricated a wooden bar which is about 35mm square, and which is made of two strips of wood (about 35mm x 17mm) which are screwed together. After fastening the two pieces of wood together, I drilled 10 holes for cell punches. these holes are slightly smaller than the diameter of the punches, and are drilled most of the way through the bar. The screws can then be adjusted to hold the two pieces of wood so that the cell punches can easily be pushed into the bar, or removed from it. Correct adjustment of the screws is very easy, and when correctly adjusted there is no risk of the cell punches falling out of the bar.
