I doubt that an eyelet punch will do the job .,.,
1. I use these eyelets ...
https://www.ebay.co.uk/itm/303715172518?hash=item46b6d5c0a6:g:L1sAAOSw7mNcd1xJ
2. I drill two side bars at a time using a pillar drill with a 4mm drill and a jig to line the holes up - then I make the frames up.
3. I insert the eyelets using a tool I made out of an old bradawl so I can pick them up on the end of it and press them into the holes, they are slightly bigger than the holes so they stay in.
4. Another jig that has the spool of wire on a spindle, a piece of 2 x 1 timber about a metre long and a peg to tell me how much wire to cut off. I use the stainless frame wire from Simon the beekeeper here:
https://www.ebay.co.uk/itm/262314484542?hash=item3d1329633e:g:TrIAAOSwDuJW1Xvq
5. Nail the first end of the wire into the side of the frame side bar next to the bottom eyelet then pass the wire through each eyelet tensioning it as you go. Pull it as tight as you can when you get to the last eyelet and nail in the side bar. The key to nailing is to drive the nail in part of the way, wrap the wire round it a couple of times then finish driving the nail in.
6. I crimp the wires using one of these crimping tools which tensions the wire fully:
https://www.ebay.co.uk/itm/284567808650?hash=item4241902a8a:g:xOYAAOSwKfVXKC01
Pretty straightforward if you are organised. You really don't need 4 horizontal wires - it's not necessary thee is suffiicient - the comb won't blow out any more with 3 wires than it will with 4 - the key to fresh comb spinning is to spin it gently and longer until the bulk of the honey is out. Another reason is that four wires adds a further length of wire which means you have more to pull through and tension - makes it harder and takes more time.
You will need a pair of wire cutters to cut the wire and a pair of pliers to help with tensioning - grip the wire with the pliers and lever against the side bar to tighten it the bend it over the edge of the eyelet which will retain some of the tension - the last pull at the end grip the wire and wrap it round the part inserted nail.
Are you going to be adding foundation or are you going foundationless ?