Varys' text:

Response: After an opponent declares a challenge, put Varys into Shadows to redirect the challenge against an eligible opponent of your choice, ignoring any Title restrictions.

Can the response be used to redirect a challenge to myself?

I guess that depends on whether you are your own opponent or not.

~I'm a bit schizophrenic when I play Melee…

That aside, I wasn't asking the question for myself, a friend of mine thought opponent was in relation to the attacker.

Nope. As you know, cards are always read from the point of view of the controller.