ok in my opinion, the first one is kind of neglecting the martial arts side of the business and the second one is the reverse, I'm assuming the second one is using the ink to symbolise the ink used with the japanese writing.
I want to say try combining the images but I'm not sure that would be enough as the ink in the wrong context could just be seen as trying to be funky or something.
Maybe look at japanese text (katakana is probably the best option here due to it's use for 'foreign' words etc) or look for a martial arts pose that could work as a dance move (I know there are some but can't think of the names).
And I just had a thought, the No. 1 in the round ring (if you take out the person) kind of looks like an old No. 7 logo where it used to be in a circle.