The vtfs contained are all painted versions of the bat.
By copying the file of your choice into a mirror directory in the tf folder (Steam\steamapps\YOURUSERNAME\team fortress 2\tf\materials\models\weapons\v_bat) and CHANGING the file's name to v_bat you will paint the bat.  Be sure to include the v_bat vmt as well, or it will be WAY TOO REFLECTIVE.

To make it so that only first person texture is painted, include the contents of the W_bat folder in a parallel folder as well.  Otherwise everyone will be carrying your painted bat.

Distinctive Lack of Hue: v bat black

Radigan Conagher Brown: v bat brown

Australium Gold: v bat gold

Indubitably Green: v bat green

Aged Moustache Grey: v bat grey

Muskelmannbraun: v bat lightbrown

Bitter Taste of Defeat and Lime: v bat lime

Peculiarly Drab Tincture: v bat offwhite

Drably Olive: v bat olive

Mannco Orange: v bat orange

Pink As hell: v bat pink

Deep Commitment to Purple: v bat purple

Dark Salmon Injustice: v bat salmon

Color Similar to Slate: v bat slate

Extraordinary Abundance of Tinge: v bat white

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BE WARNED:  IF YOU HAVE NEVER USED CUSTOM TEXTURES, READ THIS!

This is not real painting.  There are a few differences.  The biggest one is that this changes YOUR GAME FILES ONLY.  Other people will not see that your weapon is "painted".  Only you get to enjoy it

If you have multiple bats (for some reason) this will change ALL of them, as they load the same texture.

This texture only affects first person view.  when you die, or use bonk, or taunt, you will see your weapon as having the normal texture.  This is done so you don't see EVERYONE running around with your painted bat.

FINALLY, MANY SERVERS, INCLUDING THE STANDARD VALVE TF SERVERS, DO NOT ALLOW CUSTOM TEXTURES.  Test your paint first on a server you created (add new server) on the map "itemtest".  If this works, then look through your favorites and internet for servers that allow custom textures.