I have one of these, the brand is Kuhn-Rikon, you can adjust it to fit all the way down to a twist off bottle cap....it's about $25, but has saved my rear MANY times...YMMV, but it's possible that it would to what @cats5365 described.
I have a couple of new jars from WL, but did not notice if they had that same cap.
I can check tonight and see if it helps/works.
Your opener wouldn't work on the dropper bottles that usually give me the most trouble. Some of my juices come in bottles that don't catch properly, so I go for the toolbox. I use the pliers on some of those bottles that have the plastic rings that won't always split apart.
Some people's children have a rather large, Husky, rolly box in their kitchen, so there is always a tool handy when the situations arises.
My brother's friends were all jealous about the Husky box because their spouses insisted the tools had to live the the garage. Mine is the special edition Black/gold one so it does look a lot nicer than the red ones. 