I think you are describing the same way that I have cut open the paper machine wrapped rolls. I take my pocket knife (which is not really carried in my pocket outside of my farm nowadays) and I stick it through the end of the roll, without damaging the end coin, and I pull up. Most times the paper comes off in a ring. I do the same thing with the other end. This just takes a few seconds and you have a roll opened.
I have watched a lot of CRH-ing youtube videos just to see how others open their rolls and I always think to myself "you guys are going about it in a too time consuming or difficult way", most times with just their fingers. The closest I've seen someone do it to the way I do is when a youtuber used a knife, but he stuck it in the middle of the roll to undo the wrapper. I wanted to shout "no no, do the ends!"
Heck, if you don't have a knife, just get some kind of pointy metal thing like a small screwdriver even. Take your coin roll and slide the pointed metal object lightly and push it through the paper end and pop it off. Like I mentioned above, then end most times will come off as a paper ring. Now do both ends. Then the paper will release the coins. Really easy and quick.
Now unless you need to leave the rolls undamaged to use them again, this works.