No cup punch necessary, just dome the pins by peening. It takes a little practice, I recommend drilling 5 or 6 holes in some scrap material first, pin each hole, by the time you get to the last one you'll probably be pretty confident. It's not rocket science. Only time I ever use a punch is when I have a pin deep in a tight recess, usually, that's with stag. None of your pins should necessitate that, the rear, right side will be a little trickier, I'd set one head in a "pin heading vise" (make one, it takes 10 minutes), and put that head on the opposite side, then peen the tricky side, once you get a good dome all around, you can smack that side of the dome down into the low spot easily. Just focus on getting it good and even, regardless of the fact that it wont be tight in the valley, and once the high side is flush with the handle material, evenly smack that side of the pi a few more whacks and push it down in.
Another option, is to take a small cone wheel on a foredom/dremel, and remove a little bit of material around the pin hole, on the high part of the handle material there, so you have a reasonably level seat for the pin. Blend it carefully, and it will look natural.
I put domed pins in nearly every knife I make, and I joke with most of my friends that I can make domed pins quicker than they can screw together a corby in the handle material, it may be a slight exaggeration but not by much. Once you get the hang of it, it's easy as pie.
With fragile material, like real old fossil ivory, pearl, mammoth tooth, etc, the most important thing is knowing how far you can push it, and being comfortable with your pin stock. If you're concerned, select a pin material that's softer and peens easier, gold and silver (buy it in "dead soft" state) peen super easy, nickel silver isn't bad, and 410 stainless will peen all day, but it's a bit tougher. 416 will work harden and splinter if you peen it too long, and you've gotta be quick and aggressive with it before that, which encourages the pin to "upset" and swell in thickness, which is usually what causes a crack.
When making domed pins, you don't need to swell the pin internally, the domed head creates a mechanical fastener, so don't treat it like a "peened" pin that you strike off (grind flush), where you need to swell the pin inside the chamfered hole. All you need for a domed pin is to chamfer (countersink) the corner of the hole.
Make sure you chamfer the pin head before you start doming also, just take the sharp corner off, but leave the face flat, this helps keep it from splitting from excessive peening.
IMO a cup punch is only used when necessary, and it typically requires three hands when it is. You have to support the back side of the pin, preferably in another cup punch so it doesnt deform the dome, hold the knife level, hold the top punch, and smack it with a hammer, all the while, if one of these components moves or get misaligned, you're liable to put rings in, or flatten one of your pins, or worse, the handle material.