Oh, yeah, no. It's not _disallowed_ to highlight his Cool. And no, battle hardened doesn't let you roll Hard instead of Cool all the time, just for acting under fire.
So, yes, a gunlugger with battle hardened, you can still highlight his Cool, it's just impolite. And maybe he'll still get to roll it, in battle, or if there's a custom move, or if for some reason he grabbed a Cool move from another playbook.
But if I'M the gunlugger, I'm going to look at the odds of any of those things being true, and I'm going to ask my fellow player to be a pal and highlight something else instead, please.
-Vincent