If memory serves me right, I have so far only visited Skomer on three occasions, once as a day trip some time in the 1990s, more recently whilst staying on the island between the 11th and the 13th of May 2017 and finally three one-day visits, on 17 July 2018, 5 July 2022 and 11 July 2023. The Walking Notes and the Birds List both refer to the latter four.
For reference, a few websites from the Wildlife Trust of South & West Wales:
See also entry on birdingplaces.eu.
Marnix's Bird Gallery 