You will NEED The Man Who Sold the World and Venom Snake Variety to achieve this.

Thanks to HeartlessSeph, I was able to edit Snake's icon to have the mullet.

README:
This mod ONLY replaces Snake's Sortie Prep Icon along with the Avatar's icon. To play as Venom Snake, use either the rocket arm or blast arm. I'm working on re-texturing the blast arm at the moment. I also recommend renaming your Avatar at the beginning of the game to Venom Snake or whatever you want for Venom's name.

This mod requires SnakeBite Mod Manager.

[SBWM]