It is possible to walk all the way around the island simply following the beach without walking on the reef flat at all. If the tide is out, you can generally walk on the reef flat, pretty much all the way around. I suppose there may be places where it might be too uneven or too slippery, but all you have to do is go back to the beach and avoid it. The SE end is more rocky than sandy, but certainly passable by foot, but not much of a reef flat down there.
There are two inlet passages that need to be crossed to complete the entire circuit. Tatiman Passage is to the NW where the Village was, and Baureke Passage is the one to the south. Baureke passage is most often open, and sometimes closed as it was in 2001. Either way, it is a shallow crossing at high or low tide.
At high tide, Tatiman would be pretty much neck deep, so you'd basically be swimming, and between high and low tide, the current runs pretty strong through there, so low tide is really the only time you'd want to cross Tatiman on foot, and it is totally do-able, sharks and all.
If you haven't seen Mark Smith's video of crossing the channel on Youtube, you should take a look.
https://www.youtube.com/watch?v=PacL4n2Oy4cAttached is a photo of the beach on the windward side near the 7 site at reasonably low tide, a photo of the landing channel at low tide to give you an idea of how wide the reef flat can be, and a photo of me walking on the reef flat at relatively low tide with the beach behind.
I hope that helps give you and idea of the variation in conditions.
Andrew