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The Serb had been automatically listed in the draw for the tournament but said he knew it was unlikely that he would be able to gain entry into the United States.
Stakhovsky has enlisted in his country's reserve army amid Russia's invasion of its neighbour.
Zverev kicked out of the ATP 500 event in Acapulco after he smashed his racket repeatedly against the umpire's chair after a doubles defeat.
Ukrainian women's tennis players including Marta Kostyuk and Lesia Tsurenko called on the WTA to pull all tournaments from Russia following the invasion of Ukraine.
Nadal, who first won the title in 2005 and took it again in 2013 and 2020, stormed through the Acapulco draw without dropping a set, to claim his third straight title of 2022.
He beat Czech qualifier Jiri Vesely 6-3, 6-4 in the final.
The Champions League final is scheduled to be held in St Petersburg in May but sources have told Reuters that European soccer governing body UEFA is set to move the match to another venue.
Russian Medvedev will become the first player other than Djokovic, Roger Federer, Rafa Nadal or Andy Murray to top the rankings since February 1, 2004.
It was a second tour-level title for Alcaraz after his victory in Umag last year.
Djokovic said he was ready to sacrifice his shot at the Grand Slam record over the "freedom of choice" but he was keeping an open mind about taking the jab in the future.