Who says you will have to be unarmed to use unarmed skills?
You're right. It's a silly assumption that being unarmed means
not being armed.
OR have a specific Unarmed combatant weapon that is compatible with the Marshal skillsets.
Absolutely. The "unarmed" title is a little misleading as Larian planned to provide "unarmed" weapons such as knuckle dusters and claws. However, standard weapons such as swords were explicitly out-of-scope for an effective unarmed combatant.
The effect is that armed and unarmed specialisations will be incompatible.
If the skill group were labelled "marshal" or "brawler" or "grappler" or whatever and lacked the weapon-restrictions then I would definitely be more supportive of this.