You ought to use the MS Word drawing feature to create the outline as a Microsoft drawing object. You can do this within MS Word - nothing to install or download. That way you can paste it into any document you like, and since it will be a vector it will look very nicely even if you print it at poster size (Any jaggies you see on the screen will be smoothed out in the printout).
Here's how to create it in MS Word (note that these directions might be slightly off depending on your version of MS Word, but is doable regardless of your version):
1) Paste the state image into your document.
2) Make sure the drawing toolbar is visible. If it's not go to View --> toolbars and tick the Drawing checkbox. You should then see a toolbar at the bottom of the window.
3) Trace the map using a free-form shape. This menu item is found by clicking the icon that just looks like a diagonal line in the drawing toolbar, and then selecting the irregularly-shaped polygon.
4) After tracing, delete the original image of your state thereby leaving your outline. Right click on the outline and tweak the properties until you're happy.
5) Save this word document for use later as "state outline".
6) Anytime you want to use this image in a new document, open this document, then copy and paste it into the new document you want to create.
Note: Play with the toolbar elements, and play with the properties (right-click menu) of stuff you draw to see what else you can do and add. When completed select all the pieces of the drawing (hold shift key down while selecting them) then right-click and select "group". This groups all the items as a single unit which makes it easier to paste into other documents.