You better check with your zoning dept to see if you are encroaching into a required setback. Legally, to do what you propose I think you're going to be required to submit a site plan.
You might think, "oh, I'm just re-positioning something already there," was the original accessory building ever permitted? If not, you may be in for some unpleasant times, trying to move and make use of something which may-not meet the current Building Code, Land Development Code, or Zoning Code.
I would say that you need to do a permit search on your property, to see if this accessory structure was ever-permitted. If it wasn't, you need to find-out from the Building and Zoning depts. what they require to permit something new, the size of what you have there now. You don't have to tell them, "it's already there," they can see that from using Google Earth, Pictometry, or the county property appraiser's website for aerials. Get the permit history, and find out what is the process for permitting an accessory structure of the same size. Then you can make an informed decision about how to proceed.
If it was never permitted, I don't think it's going to be a happy experience for you, even if you say, "hey, I'm just moving it 30 ft.," and you do it. A nosy neighbor, a code enforcement inspector seeing something 'appear' where there wasn't anything before, a building inspector checking on another house in the neighborhood, it doesn't take much to end-up on the radar of the municipality.
Companies that sell sheds do that type of work all the time, moving sheds. Can you 'do it yourself?' Probably, but know what you're getting involved with doing, before you spend any $. The legal issues are what you need to consider, before you start moving your accessory building.
You can start here:
http://www.codepublishing.com/WA/Enumclaw/