With the Variant Human Traits option, you get to choose one skill of your choice, period.
The D&D 5e PHB on p. 31 states:
Skills. You gain proficiency in one skill of your choice.
That is the end of the description of this option. If there were meant to be a restriction to your character’s class list of skills, it would say so. But the text mentions nothing about class skill lists. So, there is no such restriction.