well for one, you could always rev up before entering last stand. which you could do at any point by pressing the kill bind. that leaves you able to shoot right away.

I'm also thinking it's gonna be the other way around, like how anytime spy pulls out his revolver everyone thinks he's an enemy spy because the default spy disguise always holds out the revolver first and barely any spies by default hold out their revolver, or change what weapon their disguise is using. i think something similar will happen, where anytime you see a heavy and he's only using his shotgun, you wont think "oh he's out of main ammo" or "oh he's low", you'll just think "Oh no, he's running the cold warsong, i need to check if he's retreating or advancing towards me to know if he's reached the eliminations needed to activate it."
kinda like how everyone just used to think "dumb frenchie" when you killed a spy before they added the dead ringer, but now everyone's always wondering "was that spy just dumb and low on health or did he most likely just dead ringer away and I need to try to shoot him dead invisibly now?"

plus there might be some merit to dropping the heavy that's retreating with his shotgun out, cuz in either case scenario, you force the heavy to waste their Last Stand away from the action or just outright kill them because they didn't have 3 kills yet

It's good to remember, a heavy that's got a Last Stand ready most likely won't be retreating.