I would think you would be fine walking or with the bus. This is a link for bus timetables on the island,
www.lesmouettes-transport.com/exec/mep.asp?NumRub=2044&Numfiche=2846 , as you can see they aren't that frequent but would be fine to use with a bit of planning. There may be other buses that operate on the island (perhaps for tourists in the summer), but sorry couldn't find anything else.
Walking some of the shorter distances between towns using the cycle paths would be no problems, and enjoyable to walk.
The tourist office website has a plan
www.iledere.com/racontez-nous/pistes-cyclables,1,1,373.php
where you can pick out bits of the cycle tracks and it will tell you how long they are, so you should be able to work out from that walking times as well.
The cycle tracks are also very good for walkers, very safe, mostly car free and on the odd sections where there are cars people do respect the cycle lanes/walkers. When we were there we picked up a detailed map of the cycle tracks from the tourist office on our first day, you had to pay for it but it was no more than 5 euro and it was well worth it, we used it every day. The island, as you probably know is virtually flat so walking or cycling isn't too difficult for different ages or levels of fitness.
Hope this is some help, I'm envious, we had a great holiday there and I would love to go back.