You might find this site useful to show you what boat trips are available. The bird-watchers' one, which will give you maximum PUFFIN time, is near the bottom of the page. Other boat firms are available, as the BBC would say, but I used to know Billy Shiels' dad and granddad!
Seahouses - Farne Islands Boat Trips
We'll be up there from 12-19 May and will definitely join the trip if it is then. May join it anyway even if it's later
If you can get to Lindisfarne (Holy Island) as well (may depend on the tides) I'd recommend that.