Technically they can stop you using the shore below HW actually (unless you are sinking) as its a NNR and the foreshore is leased off the crown estate so they can control access.
There are also other bits of Welsh shoreline that have archaic ownership that allows them to deny access to the foreshore.
Having said all that there is no real beach on Skokholm - so its a bit academic.
In terms of landing there is normally a guided walk on Mondays - otherwise generally landing was discouraged. However at the moment the island is shut as there is some major building work being planned / underway.
Anchorage is normally on the S side - you can see the jetty - its OK - but not that great - and tend to be in the tide unless quite tight in. Mostly used as a lunchtime anchorage. Skomer has much better options for overnight