recommendations ~~~

https://www.mangago.me/read-manga/gods_reborn/ (Not martial arts nor reincarnation)
https://www.mangago.me/read-manga/the_great_mage_returns_after_4000_years/
https://www.mangago.me/read-manga/mercenary_enrollment/(Not martial arts nor reincarnation)

White haired mcs are really rare to find in the action genre.. So i took my time to look something that fits your description(at my lists ofc).. but sadly only ( https://www.mangago.me/read-manga/the_great_mage_returns_after_4000_years/) is the only one that fits on you description.. I also included other manhwas that are white haired..

thank you so much, mate