Yes, if I have counted correctly, they are even a couple of weeks inside 36 years... but it's still not low enough.
Good guess... but no, not Stribling and "someone". Though Stribling was only 16 when he started his pro career, he had almost 100 bouts under his belt (and was 19 years old) when he met his first HOFer: Jimmy Slattery (who himself was 19 at the time).
McLarnin was 16, LaBarba was barely 18 when they first squared off. So we've cut it down to 34 [and within a month of 33 if LaBarba had matched him just a few weeks earlier]. They had that four rounder on October 28, 1924. LaBarba was born on September 29, 1905, McLarnin on December 19, 1907.
Using those numbers makes McLarnin 16 years, 10 months, 9 days old, and LaBarba 19 years, 29 days old, when they met - for a total 35 years, 11 month and 8 days. ... but we can go even lower!
Do amateur fights count? Tommy Hearns versus Aaron Pryor was a hell of a scrap. Lennox Lewis versus Riddick Bowe at the Olympics was alright before the lousy stoppage. I remember hearing that Ray Robinson fought Willie Pep as an amateur too.