He made his Newport debut against English side Moseley in 1897, and in his first season scored 16 tries in 24 matches, a good return for a centre.
Skrimshire was regarded as a fast and agile runner who had a cool head and good positional ability, though he was noted as being greedy with the ball and needed to release more to his wing players.
Skrimshire was first selected for Wales against England on 9 January 1899 at St Helens in front of a Welsh record crowd of 20,000.
Skrimshire was the only Welsh representative but integrated well and played in all but one of the 22 matches including all three tests against the South African team.
He finished the tour as the team's highest scorer and would later move to South Africa and played for Western Province.