Acting with "confidence" is, thus, to act with an intensive form of faithfulness, fidelity, or perhaps trust.
Is that different than acting with hope? I think that's usually how I've understood "confidence;" as a kind of self-assured belief in the better of possible outcomes... or is that what faith means?
Could it be that this definition is recursive, looping back into itself--confidence is an act of faith, faith is an act of confidence, etc.?
So I'll try a bit of a different angle on the etymology (without any recourse to citation of actual Latin sources; i.e. this is a strictly hypothetical/inductive experiment):
con= "with" + Fides = the Roman deity of trust and loyalty, whence our word "Fidelity" (See also: Fido, the loyal companion.)
Is there a difference in my version of the etymology? No, not at the most basic level, but etymology isn't a basic art. These things take finesse.
The biggest difference is that fidere, a verb, has become Fides, a proper noun. Rather than saying "trust in an intensive way," you can imagine an ancient Roman saying "I now act under the banner of Fides herself; she is with me. I present myself without trickery or deception. I am trustworthy, and my actions shall prove it." Dogs become our animal-kingdom model for confident action--loyal, true, and unashamed.
It's a different way to think about faith, isn't it? To approach the throne of grace with confidence (not sure on the Greek for that one) becomes part leap of faith, part self-recognition: I present myself without guard or covering, without hiding myself. I show myself for who I am and thus show my faith in the Father's goodness, my trust that he shall deal kindly with me.