Don't know if you've done this before so sorry if this is old news. We did this two years ago - fantastic trip, but 'ware the wind - it took us almost an extra day to cycle back to Lerwick into the south westerlies! Recommend sticking to the west coast road on the way up - it's easier and the views are great. We wouldn't bother with the tent - cut down on weight and if you are looking for cheap places to stay the bods (sort of a cross between a minimalist youth hostel and a bothy) are great - we'd recommend The Windhouse Lodge on Yell - if you can make it on the first day out it is a great base to go up to the north of Unst and back Lerwick youth hostel is great too.
http://www.camping-bods.co.uk/Windhouse-Lodge-g.asp
Don't forget to pop into the Valhalla Brewery while you're up there - you'll have to ring a head if you want a tour though and I'm not sure he'll be open all night on the 21st...