In the late 70s or early 80s getting out to Muckle Flugga, Out Stack, Foula, Sule Skerry or any of the bird sanctuaries, there were a number of skippers who would take you if you were part of, or associated with Greenpeace.
With the greater focus on protecting these reserves, it has become much harder to visit them, and the occasional tours have all but gone, so for your current visit, as you are on Unst already, your best option is to go to Haroldswick and ask at the boat haven there. Assuming the weather is appropriate, you should be able to find someone who will quote you a cost to sail past the Stack.
Be aware that there are a lot of weather and sea conditions that would preclude a journey like this – it gets pretty rough…
Credit:stackoverflow.com‘