There is a way of installing sheet vinyl without glue, and it is called perimeter-install. The vinyl is laid on the floor, much like any other floating floor (laminate, for example), and only the edges are attached to the subfloor.
Pros of Perimeter InstallationNo glue! Gluing down vinyl flooring is a sticky, smelly activity. On top of wrangling this heavy, unwieldy piece of vinyl, you have to deal with large quantities of glue. Not fun.
Cons of Perimeter InstallationThere is still some slippage, if the sheet is not installed correctly. Also, perimeter installation involves stretching the sheet slightly. Stretched vinyl is more susceptible to tears and punctures. Finally, you need to use an awful lot of staples—every two inches—and this can get tedious.
How to Install Sheet Vinyl on the PerimeterThe sheet vinyl is cut to size. Staples from a regular heavy-duty shop staple gun are driven into place ever two inches all along the perimeter. Keep the staples as close the edge as possible, but not so close that they might tear out.
The baseboards will cover the staples. In fact, you can use your baseboard to tell you how close to the edge you should staple. Be careful: these staples are hard to remove without nicking the flooring.
Absolutely no glue? Not exactly. You should still use some glue at doorways and around obstacles where staples cannot be installed.