Fold a terrycloth bath towel in half twice to make a padded surface for your bottle. Line the bathroom sink with the folded towel.
Plug the electric razor into a nearby razor-only outlet or a ground fault circuit interrupter -- GFCI -- outlet.
Turn on the razor. Tilt the razor so that the blade faces away from you. Hold the bottle upright on the towel. Use the vibration from the razor's edge -- not the blade area -- to loosen the stopper. The vibration acts as a mini jackhammer, gently knocking the wedge loose. Work the vibration slowly and carefully around the stopper and bottleneck. Stop every 15 seconds or so to check if the stopper is free.
Check the bottleneck interior and stopper for chipped glass or other debris that may have caused the parts to become stuck, once you get the stopper out. If the parts are in good condition, empty the bottle's contents into another bottle or container. Clean and dry the bottle and stopper before using them again. If any area is chipped, dispose of the contents and the damaged item.