[Cyborg17]

Doesn't cooldown time scale, too?

I'm pretty sure it doesn't.  And it doesn't actually matter because fire wait ignores cool down.  Fire wait begins to count down once the weapon has been fired.  So:

Beam 1
Fire wait:   6s
Cooldown: 1s
WarmpUp: 1s
Fire time:   2s

And
Beam 2:
Fire wait:   6s
Cooldown: .5s
WarmpUp: 1s
Fire time:   3s

Will fire at the same time assuming the AI continuously fires.  And if difficulty affected fire wait, then our primaries would be affected, too, since there's no distinction on that setting for beam weapons.

[Commander Zane]

If you want your answer on whether or not beams take less time to recharge on different difficulties quickly, mess with Shivan ships. A BFRed on Very Easy takes ten seconds to recharge before firing again, while on Insane, it's already charging up another shot just as the first shot stops firing.

[Mars]

In any case, the Collie will kill Koth faster on harder difficulties (which is tough, since that's one of the hardest missions in the game)

EDIT:

Also, remember that turret cool down is faster at higher difficulties. On Insane, turrets approach their actual rated cooldown, so Standard Flak becomes quite deadly, for instance.