Project 'Hat Bonus Activator' (for the Action Slot)

This tool (similar to the noisemaker/duels, i.e. with number of uses) give your hat bonus that doesn't affect gameplay very much. It works during N (for example, 1-5) minutes.
Here I want to try imagine possible small bonuses for each existed (at this moment) hats.

Part1.Classes and their hats.

1)Scout.
a) Batter's Helmet
b) Bonk Helm
c) Ye Olde Baker Boy
d) Baseball Bill's Sports Shine
e) Troublemaker's Tossle Cap
f) Whoopee Cap
g) Milkman
h) Bombing Run
i) Flipped Trilby
j) Superfan
k)

2)Soldier
a) Soldier's Stash
b) Stainless Pot
c) Tyrant's Helm
d) Killer's Kabuto
e) Sergeant's Drill Hat
f) Lumbricus Lid
g) Grenadier's Softcap
h) Chieftain's Challenge
i) Dr's Dapper Topper
j) Stout Shako
k) Exquisite Rack
l) Defiant Spartan
m) Hero's Hachimaki
n) Honcho's Headgear
o)

3)Pyro.
a) Pyro's Beanie
b) Brigade Helm
c) Respectless Rubber Glove
d) Triboniophorus Tyrannus
e) Vintage Merryweather
f) Attendant
g) Handyman's Handle
h) Napper's Respite
i) Old Guadalajara
j) Foster's Facade
k) Madame Dixie
l) Pyromancer's Mask
m) Prancer's Pride
n)

4)Demoman.
a) Demoman's Fro
b) Glengarry Bonnet
c) Scotsman's Stove Pipe
d) Hustler's Hallmark
e) Tippler's Tricorne
f) Carouser's Capotain
g) Rimmed Raincatcher
h) Sober Stuntman
i) Scotch Bonnet
j) Prince Tavish's Crown
k) Samur-Eye
l) Reggaelator‎
m)

5)Heavy.
a) Football Helmet
b) Officer's Ushanka
c) Tough Guy's Toque
d) Hound Dog
e) Heavy Duty Rag
f) Hard Counter
g) Pugilist's Protector
h) Cadaver's Cranium
i) Dealer's Visor
j) Coupe D'isaster
k) Big Chief
l) Magnificent Mongolian
m) Dread Knot
n)


6)Engineer.
a) Mining Light
b) Engineer's Cap
c) Texas Ten Gallon
d) Texas Slim's Dome Shine
e) Hotrod
f) Safe'n'Sound
g) Buckaroos Hat
h) Industrial Festivizer
i) Big Country‎
j) Professor's Peculiarity‎
k)

7)Medic.
a) Prussian Pickelhaube
b) Otolaryngologist's Mirror
c) Vintage Tyrolean
d) Gentleman's Gatsby
e) Ze Goggles
f) Berliner's Bucket Helm
g) German Gonzila
h) Geisha Boy
i) Medic's Mountain Cap‎
j) Grimm Hatte‎
k)

8)Sniper.
a) Trophy Belt
b) Master's Yellow Belt
c) Professional's Panama
d) Ritzy Rick's Hair Fixative
e) Shooter's Sola Topi
f) Bloke's Bucket Hat
g) Ol' Snaggletooth
h) Larrikin Robin
i)

9)Spy.
a) Fancy Fedora
b) Backbiter's Billycock
c) Magistrate's Mullet
d) Frenchman's Beret
e) Familiar Fez
f) Détective Noir
g) Noh Mercy
h) Private Eye‎
i) Charmer's Chapeau‎
j)

0) All-class.
a) Cheater's Lament
b) Ghastly Gibus
c) Mildly Disturbing Halloween Mask
d) Bill's Hat
e) Max's Severed Head
f) Modest Pile of Hat
g) Noble Amassment of Hats
h) Towering Pillar of Hats
i) Alien Swarm Parasite
j) Ellis' Cap
k) Mann Co. Cap
l) Wiki Cap
m) Ghastlier Gibus
n) Horrific Headsplitter
o) Horseless Headless Horsemann's Head
p) Spine-Chilling Skull
q) Voodoo Juju
r) Halloween Masks
s) Saxton Hale Mask
t) A Rather Festive Tree
u) Bounty Hat
v) Treasure Hat
w) Hat of Undeniable Wealth And Respect
x) World Traveler's Hat
y) Athletic Supporter
z) [ classified ]
aa) Humanitarian's Hachimaki
ab) Benefactor's Kanmuri
ac) Magnanimous Monarch
ad)

Part 2. Examples.

1a) enemy's Sandman Ball's long-range attacks affect you like they are short-range;
6e) +1 metal from dropped weapon;
6c) you can "Cow Herd&" enemy's sentry;

/to be continued.../