[Build: 0.8.22] Seems that you don't need to be on the 'Ninja Stylin'' quest for the ninja outfits to appear for ordering at Kohaku's shop.

[Papum]

I tried going to Kohaku's shop and the order ninja outfit option appeared even though i had not gotten the Ninja Stylin' quest through having defeated Kurako and talked to her about it.

 

[Aury]

I think this might be intended? I may be wrong, but it’s been this way for years; my understanding was that asking Kohaku first was simply an easier on-ramp.

 

[Papum]

Probably as you do get the quest anyway.
I always get it through defeating Kurako, so never knew this could also be possible.