I have done sheet metal work for years, and yes...pop rivet gun will work. Even a cheap one. I would not spend the extra money for a new one if you have one in the shop.
Two things to do:
1. Buy extra cherry rivets. Pull one in a scrap chunk of the same thickness. If the stem breaks just below, level or a tad high...you are good to go. Extra cherries are nice to have.
2. Great idea on the over sized cherry. Remember to get a #27 drill to clean up the hole for the over sized -4 rivet. If the #27 drill is just too big to go in the hole...it might be better to stay with the standard size.
Oh...one last thing, keep your fingers out from between the puller levers. When that stem breaks off and you pinky finger is in the way
there is only pain.
If you need a drawing of the stem limits or if you need to know how to remove a cherry...email me and I'll see what I can do.