In 2014, as a freshman at Wake Forest, he appeared in 27 games in relief, going 4–1 with a 2.17 ERA.[3] As a sophomore in 2015, he went 5–3 with a 2.89 ERA in 71+2⁄3 innings which were split between starting, closing, and long relief.[4] After the 2015 season, he played collegiate summer baseball with the Chatham Anglers of the Cape Cod Baseball League, and was named a league all-star.[5] In 2016, Dunshee's junior year, he pitched to a 10–5 record with a 3.20 ERA in 16 games (15 starts).[6] After his junior year, he was drafted in the 14th round of the 2016 Major League Baseball draft by the Chicago Cubs.[7] However, he did not sign and chose to return to Wake Forest for his senior year.[8] During his senior year, he started 17 games and went 9–1 with a 3.91 ERA, helping lead Wake Forest to their first super regional appearance since 1999.[9] After his senior year, Dunshee was drafted by the Oakland Athletics in the seventh round of the 2017 Major League Baseball draft.[10]
Dunshee did not play a minor league game in 2020 due to the cancellation of the minor league season caused by the COVID-19 pandemic.[21] To begin the 2021 season, he returned to the Aviators, now members the Triple-A West.[22] After five starts, he was placed on the injured list with a collarbone injury.[23] He was activated in early September.[24] Over ten games (nine starts) with the Aviators for the 2021 season, Dunshee went 1-5 with a 6.65 ERA and 38 strikeouts over 43+1⁄3 innings.[25]
Dunshee returned to Las Vegas for the 2022 season.[26] Over 31 games (twenty starts), he went 5-11 with a 9.22 ERA and 92 strikeouts in 111+1⁄3 innings and led the minors in home runs allowed with 38.[27] He made one appearance for Las Vegas in 2023, allowing two runs in an inning of work before he was released on April 14, 2023.[28]
San Francisco Giants
On April 24, 2023, Dunshee signed a minor league contract with the San Francisco Giants organization.[29] He split the season between the Double–A Richmond Flying Squirrels and Triple–A Sacramento River Cats. In 23 games for Richmond, he logged a 2.56 ERA with 22 strikeouts; in 10 games for Sacramento, he posted a 3.93 ERA with 10 strikeouts. Dunshee elected free agency following the season on November 6.[30]
Atlanta Braves
On January 31, 2024, Dunshee signed a minor league contract with the Atlanta Braves.[31][32] In 27 appearances split between the Double–A Mississippi Braves and Triple–A Gwinnett Stripers, he accumulated a 2.30 ERA with 66 strikeouts and 4 saves across 47 innings pitched. On August 8, Dunshee was selected to the 40-man roster and promoted to the major leagues for the first time.[33] He debuted that day against the Milwaukee Brewers, allowing five runs with three strikeouts in 2+1⁄3 innings. Dunshee was designated for assignment by the Braves on August 14.[34] He cleared waivers and was sent outright to Gwinnett on August 16.[35]