Selected by the Avalanche in the fifth round (125th overall) of the 2017 NHL Draft, Shvyrev, 19, split the 2017-18 campaign with Metallurg Magnitogorsk of the KHL and Stalnye Lisy Magnitogorsk of Russia's junior league, the MHL. He registered 17 points (5g, 12a) in 10 games with Stalnye Lisy and tallied one point (1g, 0a) in 32 outings with Metallurg, his first career KHL point. The Magnitogorsk, Russia, native competed in the KHL's postseason for the first time in 2017-18, skating in three contests.

Shvyrev has played for both Metallurg and Stalnye Lisy for the last four seasons and has totaled 133 points (39g, 94a) in 113 career MHL contests and has 12 points (4g, 8a) in 20 total postseason games. The 6-foot-1, 192-pound center represented his country at the 2015 Ivan Hlinka Memorial Tournament, where he tallied one point (0g, 1a) to help Russia capture the bronze medal.