Fist rules (LRB pg.24) state: "Note: The following rule only apply to warriors who have lost their weapons. Creatures such as Zombies, animals, etc, ignore these rules. Warriors using their fists can only ever make 1 attack."
I'd say that a Possessed Mutant is very much a "creature such as zombie" -> you do not use fist rules nor do you suffer the penalties stated in fist rules. Though the model started as a weapon-wielding warrior, a Shadowlord decided otherwise and now the model is a Possessed for most intents and purposes.
-Touko / Squirreli