*Club domestic league appearances and goals, correct as of 15:17, 29 November 2024 (UTC) ‡ National team caps and goals, correct as of 21:15, 20 October 2023 (UTC)
Scrimshaw began his career at AFC Bournemouth, joining them at the age of 15 following a trial with the club.[3] He spent the 2018–19 season on loan at Poole Town, scoring 17 goals in 23 games in all competitions for the club.[5] Following the loan spell he was praised by the club's manager,[6][7] and turned professional with Bournemouth in June 2019.[4]
He moved on loan to Eastleigh in January 2020,[8][9] making 10 appearances in all competitions,[5] and signed a new two-year contract with Bournemouth in July 2020.[10]
On 8 January 2021, Scrimshaw joined Newport County on loan until the end of the season.[13] He made his debut for Newport in the starting lineup for the 0–0 draw against Salford City in League Two on 16 January 2021.[14] Scrimshaw scored his first goal for Newport on 23 January 2021 in the 3-2 League Two defeat against Oldham Athletic.[15]
On 26 August 2022, Scrimshaw joined National League side Yeovil Town, signing a two-year deal.[18][19] On 6 January 2023, Scrimshaw left Yeovil via mutual consent having played eight times.[20]
On 21 February 2023, Scrimshaw signed for National League side Eastleigh on a short-term deal.[21] He was released at the end of the season.[22] He then signed for AFC Totton in July 2023.[23]