The Channeling Execution text: "Once this High Magic has been purchased, the character may Killing Blow using any one valid Channeling effect they have available by spending 5 Channeling points. This Killing Blow may be performed using any valid mechanism available (for example, a weapon they are wielding or their hands)." Emphasis is mine.
The effects you have available are dependent on your available sources. As long as you have a wand or relic of the flavor you which to killing blow with, you may use that element. In short, you can freely choose between different elements with a single purchase of Channeling Execution.