There is nothing in the Magic Tournament Rules about timing when interrupting a shorcut. All it says is "A player may interrupt a tournament shortcut by explaining how he or she is deviating from it or at which point in the middle he or she wishes to take an action." So there is no reason you wouldn't be able to have a moment to think about it.

Obviously if you do anything that acknowledges the attack as being valid like casting your Kill Shot or otherwise using priority it is too late to deny them their shortcut. Anytime prior to this point though should be fine, as long as you don't fall into Slow Play territory.

Personally, if I were Nathan what I would do in this situation is when Anthony declares attackers say "Wait, I might have something before declare attackers" and then once I have taken a moment to decide what to do either say "Ok, go ahead" or "Before declare attackers I..."

There is nothing in the Magic Tournament Rules about timing when interrupting a shorcut. All it says is "A player may interrupt a tournament shortcut by explaining how he or she is deviating from it or at which point in the middle he or she wishes to take an action." So there is no reason you wouldn't be able to have a moment to think about it.

Obviously if you do anything that acknowledges the attack as being valid like casting your Kill Shot or otherwise using or passing priority it is too late to deny them their shortcut. Anytime prior to this point though should be fine, as long as you don't fall into Slow Play territory.

Personally, if I were Nathan what I would do in this situation is when Anthony declares attackers say "Wait, I might have something before declare attackers" and then once I have taken a moment to decide what to do either say "Ok, go ahead" or "Before declare attackers I..."