I've found that the koryu that I train in is, in fact, the best conditioning for the koryu that I train in. Running helps with building up endurance, but that doesn't always transfer over-- running tends to be aerobic, and our kata tend to be extremely anaerobic. Weights also help with giving me a baseline of strength, but they don't necessarily prepare me for holding an extremely beefy bokken in static poses for long periods of time. Also, the way that I use my body to curl a dumbbell doesn't correspond at all to the way that I'm supposed to use my body to swing a sword, and sometimes weightlifting even leads to a bad habit of trying to use tense shoulders to muscle something that should come from an entirely different area.
David Sims
"Cuius testiculos habes, habeas cardia et cerebellum." - Terry Pratchet
My opinion is, in all likelihood, worth exactly what you are paying for it.