White Walkers can be eliminated by using fire. However, there are some cases that happened (in the series), where the Night King either walked right through it or the radiance of their coldness are far superior than the dragon fire's strength. (I have no idea whether a dragon's fire is just a normal fire).
Wildfire has been used to defeat Stannis and his alliances when he invaded King's Landing. Wildfire caused explosions that burned Stannis' fleet. Wildfire even surpassed a normal fire since its strength cannot be diminished by the water.
With the level a Wildfire has, is the Night King still able to walk through it? As far as I know, Wildfire can cause worse damages than normal fire.
Note: I haven't read the books yet.