Szczechura grew up playing hockey in his hometown of Brantford playing minor hockey for both the Brantford Saints and Brant Bandits AAA hockey programs.[citation needed] He played in the 1999 Quebec International Pee-Wee Hockey Tournament with Brantford.[3] After being drafted in the 11th round of the 2001 OHL Priority Selection by the Barrie Colts, Szczechura decided to pursue an NCAA scholarship and played three seasons with the Brantford Golden Eagles of the OHA Midwestern Ontario Jr.B. League.[citation needed] He accepted a scholarship to Western Michigan University in 2003.[citation needed]
Previously, Szczechura played for Western Michigan University (CCHA), the Iowa Stars (AHL) and the Norfolk Admirals (AHL). He signed with the Lightning as a free agent on April 24, 2008, and debuted against the Philadelphia Flyers on December 2, 2008. He scored his first NHL goal against Tim Thomas of the Boston Bruins on December 8, 2008.[4] Szczechura scored his second career goal and assisted on another Lightning goal on December 23, 2008 against the Pittsburgh Penguins, and was named the first star of the game. He was later signed by the Buffalo Sabres to play with their AHL affiliate, the Rochester Americans. On November 26, 2011, the Sabres recalled Szczechura.[5]
On May 22, 2012, it was announced that Szczechura signed a one-year contract to join Czech team, HC Lev, for their first foray into the Kontinental Hockey League.[6] Szczechura appeared in three games to start the 2012–13 season, before losing his place in the high flying Lev squad. On September 26, 2012, Szczechura signed contract to transfer over with fellow KHL, club Dinamo Riga.[7] After two seasons, in May 2014 he signed a two-year contract with HC Dinamo Minsk.[8] After his contract had expired, he moved fellow to KHL outfit Traktor Chelyabinsk, signing in May 2016.[citation needed]
As a free agent from Chelyabinsk after three seasons, Szczechura extended his KHL career in agreeing to a one-year contract with his fifth KHL club, Torpedo Nizhny Novgorod on July 16, 2019.[9]