Weapon-specific-ness of pirate skills?

Most infighter skills can be used with no weapon at all. Pretty weird to think about but that's how it works.

Somersault kick works with a gun, and any other weapon. Straight works with a gun too. I think they stop working with guns after first job, though.

Did this mean that somersault kick, etc, wont work after first job with other weapons, or that all the skills after second job dont work? Because having a pumpkin spear or something second job at CPQ for a while might be good, because of the atk boost. At least until mastery and booster is gotten and points start going into screw punch.