Stovell played for Bermuda in both the 2001 and 2003 editions of the ICC Americas Under-19 Championship. He was named the man of the match in a 2003 match against Argentina, having scored 204 runs out of Bermuda's total of 364. Bermuda won the match by 302 runs. Stovell was selected in Bermuda's squad for the 2011 World Cricket League Division Two in the United Arab Emirates. It was during this tournament that Stovell made his List A debut against Papua New Guinea. On debut he took two wickets and scored 42 runs. In Bermuda's second match against Hong Kong he took his career-best List A bowling figures of 3/25. In a match against Namibia, Stovell scored 73 runs, the most of the match for Bermuda, but Bermuda still lost the match by 86 runs after being bowled out in the 43rd over. Bermuda's coach, David Moore, expressed disappointment after the match that Stovell hadn't stayed in for longer. In the next match against the United Arab Emirates Stovell again top-scored for Bermuda with 77, his highest List A score, but again Bermuda failed to win. Stovell finished the tournament as Bermuda's leading run-scorer and also took the second-most wickets, but Bermuda finished the tournament in last place and were relegated. Stovell was selected as part of Bermuda's squad for the 2012 World Twenty20 Qualifier, also in the United Arab Emirates. In his Twenty20 debut for Bermuda against Denmark he scored 56, still his highest score in a Twenty20 match. Later in the tournament he also took his career-best bowling figures of 4/25 from 4 overs against Nepal. He was Bermuda's leading wicket-taker for the tournament with 14 wickets at an average of 16.42 runs per wicket, and he was also their most economical bowler, only conceding 6.38 runs per over. In 2013 Stovell played for Bermuda at both the World Cricket League Division Three in Bermuda and the World Twenty20 Qualifier in the United Arab Emirates. In the WCL Division Three he struggled with the bat and only scored 52 runs at an average of 10.40. In the opening match of the World Twenty20 Qualifier he was named the man of the match as Bermuda's top run-scorer, but he only finished the tournament with a batting average of 14.12. He played seven matches for Bermuda in the 2014 World Cricket League Division Three and six matches in the 2016 World Cricket League Division Four. In April 2018, he was named as the vice-captain of Bermuda's squad for the 2018 ICC World Cricket League Division Four tournament in Malaysia. He was the leading wicket-taker for Bermuda in the tournament, with twelve dismissals in six matches. In August 2019, he was named as the captain of Bermuda's squad for the Regional Finals of the 2018–19 ICC T20 World Cup Americas Qualifier tournament. He made his Twenty20 International debut for Bermuda against the Cayman Islands on 25 August 2019. In September 2019, he was named as the captain of Bermuda's squad for the 2019 ICC T20 World Cup Qualifier tournament in the United Arab Emirates. In November 2019, he was named in Bermuda's squad for the Cricket World Cup Challenge League B tournament in Oman.
