All tests done with 212 Stamina

Fast Swords: (11 attacks in ~5.8 seconds)
Pipe of Thralldom
Queenslayer Blade
Argent Wolf Blade
Executioner

Normal Swords: (11 attacks in ~7.3 seconds)
Hanemukuro
Enduring Crimson
Blazing Claw
Iceblood
Sunset Sword

Fast Heavy Swords: (9 attacks in ~5.8 seconds)
Lost Broad Sword

Normal Heavy Swords: (9 attacks in ~6.4 seconds)
Black Saber
Broad Sword

Slow Heavy Swords: (9 attacks in ~7.1 seconds)
Machete

Normal 2H Swords: (6 attacks in ~5.6 seconds)
Queenslayer Greatsword
Nagimukuro
Warped Blade
Black Great Sword
Judgement Edge
Sunset Great Sword
Oni Bane

Slow 2H Swords: (6 attacks in ~6.5 seconds)
Zweihander
Argent Wolf King's Blade
Lost Zweihander
Argent Wolf Brand

Fast Halberd: (8 attacks in ~5.6 seconds)
Black Halberd
Impaler

Normal Halberd: (8 attacks in ~6.2 seconds)
Bardiche
Lost Bardiche
Obliterator Axe

Slow Halberd: (8 attacks in ~6.6 seconds)
Queenslayer Halberd

Spinny Halberd: (8 attacks in ~8.0 seconds) Has a multihit attack but damage seems comparable to single hit; I've counted it as 1 attack
Garnet Splitter
Assassin's Sickle
Sunset Halberd
Argent Wolf Poleaxe
Dammerung

Fast Axe (Hammer): (6 attacks in ~5.7 seconds)
Heavy Axe
Lost Heavy Axe

Normal Axe (Hammer): (6 attacks in ~6.0 seconds)
Tyrant's Labrys

Fast Hammer: (5 attacks in ~4.9 seconds) I tested the 6th hit speed and it's ~5.9 seconds
Huge Hammer
Burned Warhammer
Argent Wolf Warhammer

Normal Hammer: (5 attacks in ~5.3 seconds)
Queenslayer Hammer
Hammer of Thralldom
Sunset Hammer

Slow Hammer: (5 attacks in ~6.0 seconds)
Juggernaut Sledgehammer
Impulse Anchor

Fast Bayonet: (12 attacks in ~7.6 seconds)
Queenslayer Bayonet
Brodiaea
Burning Disaster
Sunset Bayonet
Black Bayonet

Normal Bayonet: (12 attacks in ~8.0 seconds)
Bayonet
Lost Bayonet

Slow Bayonet: (12 attacks in ~8.5 seconds)
Riot Breaker
Argent Wolf Bayonet

Spinny Bayonet: (12 attacks in ~10.5 seconds) Has a multihit attack but damage seems comparable to single hit; I've counted it as 1 attack
Rubellite Piercer