Reynolds, the Canadian-American actor best known for playing the wisecracking antihero 'Deadpool', leaned into the controversy in the 59-second video released on Thursday.
Emerging from behind a tree alongside McElhenney, Reynolds says: "Today, for no particular reason, we want to talk about the importance of privacy."
"Specifically how to prevent spies from seeing what you're doing on the internet," adds McElhenney, best known for his role in television comedy 'It's Always Sunny in Philadelphia'.
"There's some things that you just don't want any other people to see ..." Reynolds continues, before later adding: "Privacy - that's important to people everywhere," as the pair reference Oxford United, Ipswich Town and Middlesbrough, clubs whose training sessions Southampton were accused of observing last season.
The pair later highlight Firefox's privacy features, with Reynolds remarking: "Refreshing, huh? An organisation that actually respects your privacy."
The joke was a nod to the "Spygate" row that erupted in May after Middlesbrough complained of unauthorised filming at their training ground.
The Football League charged Southampton, who were later expelled from the Championship playoffs after acknowledging they had observed opponents' training sessions within 72 hours of matches.
Middlesbrough, who lost to Southampton in the play-off semi-finals, were reinstated in the final, where Hull City ultimately secured promotion to the Premier League.
The Football Association subsequently launched its own investigation and has alleged Southampton spied on opponents multiple times between December 2025 and May 2026.
Reynolds and McElhenney bought the Welsh club in 2021.
Wrexham sit 19th in the Championship, while Southampton are ninth after seven matches.