Tom:
There's certainly no Carnauba wax or acrylic floor finish on Peel&Stick tiles; all you have is a clear vinyl wear layer on top.
But, to do this right, what you should be doing is buying a bag of cement based floor leveling compound (and I prefer Mapei Planipatch and was using it long before there even was a Home Depot in Winnipeg to sell it), and put two coats of floor leveler down before sticking your new tiles down.
The whole purpose of the floor leveler is to fill in the surface embossing for the old tiles so that the embossing doesn't eventually end up "telegraphing" throught and shoing up as a "ghost pattern" on the new tiles.
If you don't have any embossed pattern on your old tiles, you don't need to bother with the floor leveler. Also, if it wuz me, I would install the tiles offset at least 2 inches in both directions from the old tiles. Use a tape measure to ensure that your new starting point doesn't result in your having to cut thin pieces of tile to fit up to any wall or toe kick.
With Mapei Planipatch, you should mix your first coat of Patch with Mapei's recommended "additive" (pronounced "adhesive", which is called "Planipatch Plus"). You spread that on your existing floor with an ordinary plastering trowel, wait for it to dry, and then with a bright light on the floor, scrape off any trowel ridges or drops of patch with a sharp paint scraper.
Don't mix up more patch than you can spread in 15 minutes cuz it'll harden up on you so that you can't spread it. I use 7-11 Big Gulp cups to mix the patch in.
Then, for the second coat of patch, dilute the additive with 3 parts water and use that solution to mix the Planipatch. Then, scrape that second coat down, and you're ready to start sticking the new tiles down.
When I do this kind of work, (and I;ve done more than my fair share of it) I put a third coat on:
- I mix the Planipatch with water only so that it dries soft
- Then I sand the whole floor surface down smooth with a drywall hand sander and sanding screen so that it's smooth as a baby's bum,
- Then I paint the Plus additive onto the third coat with a 10 inch paint roller. The additive gets wicked into that soft third coat and glues all the particles of cement together as it dries. I then have a SMOOTH, HARD surface on which to install my vinyl composition floor tiles.
But, you don't really need to do that. As long as you scrape the floor smooth with the aid of a sharp paint scraper and bright light (to exagerate any roughness and make it easily visible), then you're doing the job the same way as any pro would (if a pro would stoop to installing Peel&Stick).
Alternatively, put the first two coats on as described, and then use my method over any rough spots you still find to smooth them out.
Use 2 inch painter's masking tape around your baseboards to avoid getting floor patch all over them. In fact, depending on the style of baseboard you have, you'll need to remove the shoe molding or the entire baseboard. It's the baseboard's or shoe molding's job to cover the cut edge of any flooring you install in the room, so you'll need to remove the last molding to be installed, and then re-install it to cover the cut edge of your new P&S tiles.