Actually, Kansai-style oden usually uses konbu-dashi (soup stock made out of seaweed)... I've never heard of Kansai-style oden made primarily with chicken soup stock (that's certainly not how my Kansai-jin mother makes!). It is light in color because of the konbu-dashi. Kanto-style, I think, uses bonito-flakes (katsuobushi) and adds LOTS of soy sauce.
Either way, I doubt most oden places use primarily chicken soup stock as the main base--it's either konbu or katsuo, and sometime mixed with other soup stock ingredients. But if you want to make sure, you can ask the restaurant beforehand what they use for their dashi.