There is a better way.
Take a regular dress shoe, presumably with leather soles and heel.
Put the bottom of the wine in where your foot would go, sticking up as though it was your leg.
Holding them together with the wine now horizontal, bump the heel of the shoe against the wall, or some firm vertical surface that won't suffer from the bumping.
Using the right pressure, the cork will work its way out enough to grab and pull the rest of the way.
Current Alfa: 1986 Spider Veloce
Previous Alfa: 1987 Spider Graduate