From the Compendium:
The group winning the In Sight will now act. Each figure will act, in order from top to bottom:
- If cannot fire, will Charge into Melee if within
6”, otherwise Carry On.
- If in Duck Back, will recover to Carry On.
- If Hunkered Down:
- Can recover to Carry On if Rallied (page
- If not contacted, remain in Hunker Down.
It doesn't look like you can. I figure "having" to shoot back after winning an In Sight is just part of the chain reaction system. It's a reaction rather than active fire, like in Ed's example in this thread.
However, I saw this example in the Compendium too:
Hunkered Down Harry (Rep 4) is fine with
hiding out until the shooting stops. Sgt. Billy Pink is
active and leaves cover causing an In Sight.
Winning the In Sight he continues his move to Harry.
Shooting after winning an In Sight is consider "inactive" fire, yet here Sgt. Billy Pink in the example just "decides" not to react.