Madcatz TES+ SFV Shadoloo Mod

Hey everyone!
Can any of you guys please tell me if the Hayabusa Joystick will fit inside of my Madcatz SFV Shadoloo TES+ ? I want to swap my Sanwa JFL with Hori's (Don't get me wrong, I think Sanwa is great but I've been itching to try the Hayabusa lever for a while due to it's positive feedback). If it doesn't fit, what modding will I have to go trough in order to do so? I have been hitting my head against the wall with this one and haven't found anything on the internet.

Thanks!