If anyone wants to make a mod that changes the texture or sound effects of the sword, feel free to do so.
Sound effects should be in a subfolder of the mod named LoadedSoundEffects, and the following sound files will be read if present:
Sword_Hit_Soft.wav
Sword_Hit_Hard.wav
Sword_Hit_Wall.wav
Sword_Swing.wav
Sword_Parry.wav

To make a custom texture, simply copy the assets folder from this mod into your mod and change the .png file in assets/SwordMod. Note: You MUST keep the .txt file. Just copy the .txt file and leave it unchanged (unless you know how to work with atlas data).

Copy/pasted poorly-written explanation:
How to use:
The SwordMod_Sword.png and SwordMod_Sword.txt files will stay the same and will be the default sword texture.
Additional textures can be added by making files in the format SwordMod_Sword[x].png (where [x] == literally anything), like:
SwordMod_Sword2.png
SwordMod_Sword3.png
SwordMod_Sword_Galatine.png
etc.

These textures should JUST be the top-left part of the atlas (you can exclude the sandbox unlock), that is, the sword as it shows up in-game. You don't need .txt files for any swords except the first one. Try looking at my Lightsaber mod as a reference.