The route Okami used in his 50 star WR hits the Wing Cap Switch and uses the cap for overworld movement. While doing the overworld movement without the Wing Cap is slower, it saves time overall to replace the Wing Cap Stage with a faster star. This is a route based around this change:

C2 > C4 > C5 > C9 > G5 > C8 > Reset > G1 > G3 > G2 > C3 > C1 > C7 > C6 > B1 > Save + Quit > B2

It might be unclear how to go through this route without the Wing Cap, so here's a video showing the different overworld movement:

If you're wondering what specific stars I get in my runs, I have a Google Doc of them here: https://docs.google.com/document/d/1BRo_4QkhV4V1JpmqtzScYcT7OC_vvlDpmK_J7RpyzRI/edit?usp=sharing

I haven't compared the stars rigorously enough to know if these are the absolute fastest, but it should be pretty close.