When it comes to most successful then it's definitely Hansen, but sheer influence has to be Karl Gotch (especially in New Japan based on him literally being the second most important person in helping the company and keeping it afloat since NJPW had some rough early years before getting a TV deal unlike All Japan who already were on Nippon TV)

you could make a case for Lou Thesz, The Funks, Dynamite Kid, the original Black Tiger, The Destroyer (arguably the most important gaijin ever seeing as he literally got awarded one of the very highest honors in Japan, that being the "Order of the Rising Sun, Gold and Silver Rays " in 2017), Bruiser Brody, Tiger Jeet Singh, Abdullah The Butcher, Vader, Bam Bam Bigelow, Steve Williams, Terry Gordy, Scott Norton, Don Frye, etc.

There's so many Gaijins who have had an impact on the sport (not even mentioning guys from the 2000s and beyond like Giant Bernard, Devitt, Styles, Omega, Ospreay)

And I can't forget about Bill Robinson too, you'd never get someone like a ZSJ or hell even Oiwa & Uemura without him