I personally wouldn't say it's perfect, but certainly still worth the trip. If you've not photographed puffins before then one thing you should be aware of is how small they are; they're smaller than most people who've never seen on in the flesh imagine. Which basically means you end up needing a longer lens than you might think despite the close proximity.
You can get some closer shots with the occasional puffin on Staple island with your setup. I personally think Inner Farne for puffins with a 70-200 + 1.4x + sensor crop is still too shot to get near to filling the frame (the best location for puffins on that island, in my experience, is a 400 + 2x + sensor crop shot).
Your setup should however let you get some decent puffin flight pictures on both islands, and is ideal for the terns on Inner Farne. You could probably take the converter off for that.
You don't need anything long at all for the shag on Staple island; if anything you can get some stunning wide angle stuff if they nest in the right locations.