Hi, Lauren. Your hardware store is right on track for most paper, but there is an easier way with vinyl paper. Vinyl paper has a vinyl top layer and a paper bottom layer. If you use a utility knife and can separate the layers, pull the vinyl off, then use the vinegar and water on the paper, you will be way ahead. You probably will have no problem finding a seam somewhere where the paper is slightly loose. Five year olds are particularly adept at this and can pull the vinyl off starting from any little seam--ask me how I know.
Just as a point of information, there is a tool called a "paper tiger" that is made for scoring the regular paper and will also work on vinyl, the other method is just easier.
I am glad to hear that the hardware store was suggesting vinegar and water. There are products like DIF and Dissolve that are made for this but I have had good luck with the vinegar. Use cheap white vinegar and hot water applied with a sponge. Let it soak for a while and you should be able to scrape the paper backing off easily with a metal or plastic putty knife. Then rinse with plain water and another sponge. Have lots of trash bags around for the vinyl and residue.