For an axolotl that has a mild case of fungus, would fridging be sufficient enough without the need of salt/tea baths?
Fridging is generally reserved for emergency situations such as high temps, impaction, extreme constipation, etc. It's unlikely to help at all with fungus. What will help are frequent water changes (tubbing MAY make this more efficient, or it may not, depending on your situation). This is the most important treatment. I've personally had positive experiences with tea baths, but their effects are debatable. I would try tea baths before salt baths as salt baths are a more extreme, dangerous, and potentially painful experience for your axolotl. They are, however, more effective, so if the water changes and tea baths don't take care of it within a few days, a couple of salt baths should.