Going through the timing chart for performing an attack, the first step is to declare a target and measure to check range and firing arc.

At this point, if the current ship activating has a valid target in range for (let's just say) it's primary weapon... can the player than choose NOT to attack at this point in the phase?

Specifically this came up with Ahsoka and Captured TIE. IF she measures to an enemy ship with the range ruler and finds that it is indeed in arc and within range for a primary weapon attack, can the player now decide to not perform the attack, thus allowing the Captured TIE card to remain face up?

I believe the answer is yes.

A week ago in a match I felt the other way. But I really just want to know for future reference.

Page 22 of the current FAQ under COMBAT. A player can choose not to attack. Since there are no restrictions on the timing of this choice, I think you could measure range and arc and then decide against attacking.

Yeah nothing in the rules say you must attack if you're able, so there's no reason you can't measure range and then decide not to attack at all.

Yup.

Worth noting that you can measure range and arc to every enemy ship on the board before deciding which, if any, to attack. But you can only measure from the currently active ship, resolve its attack (or not) then move on to the next active ship.