[4] After his selection in the 2017 NHL Entry Draft, Skinner was later signed to a three-year, entry-level contract with the Edmonton Oilers on May 14, 2018.

[5] Entering the final year of his entry-level contract, Skinner remained on the Oilers roster to start the pandemic-delayed 2020–21 season.

[6] He made his NHL debut and first career start on January 31, 2021, against the Ottawa Senators, collecting his first win in an 8–5 victory.

On February 14, 2022, Skinner recorded his first NHL shutout against the San Jose Sharks, making 20 saves to win the game 3–0.

[9] During the 2022–23 season, with the departure of Mikko Koskinen and injury to Mike Smith, Skinner was initially expected to be the backup to newly signed goaltender Jack Campbell.