There are degrees of "Weeaboo Fighting Magic" on the martial initiator spectrum, from the hilariously supernatural to the only moderately extraordinary, depending on the class and disciplines one focuses on.
Warlord is the least blatantly "magical" class of them all, and that's the one we're leaning toward, plus the Golden Lion discipline is quite mundane, too.
Also, since we're limited to 6th character level in this setting, martial initiators can only learn maneuvers up to 3rd level. That puts a heavy limiter on even the really supernatural disciplines, like Riven Hourglass and Veiled Moon. There won't be any teleportation shenanigans to make someone hit themselves with their own attack or permanently banishing an enemy to the Astral Plane if they fail a Will save.
IIRC, the most magical thing a Golden Lion initiator can do using 3rd level and lower maneuvers is to use a Counter maneuver to pit their Diplomacy check against an enemy's attack bonus to protect a nearby ally from an attack.