Might anyone have suggestions beyond the tedious task of dragging and dropping each clipping into an AppleWorks document and using Get Info -> Open with to set the application to Pages?
As your query focuses on an onerously repetitive task, I suspect the Automator (or scripting) route Virtual1 suggested might be more immediately worthwhile looking into than conversion options that most likely won't directly (if at all) affect your Clippings repository. (You don't mention whether you intend to deal with all or part of your Clippings repository specifically or with documents containing clippings, but I suspect the former.)
Since there doesn't seem to be an export option for clippings, and it isn't clear which app other than AW can open them (e.g., neither GraphicsConverter or Illustrator works), one way of preserving them is to collect them in appropriate AW documents (word proc., spreadsheet, database, image etc.) and convert those. It may be possible to combine clippings classes in a single file, but the ability to manipulate them separately depends on the app you're eventually going to open these files with. Whichever approach is selected, this collection stage would benefit greatly with automation.
One thing to be careful about, however, is that changes to the resolution or editability of the clippings by the receiving/converting app are possible, and these changes are best assessed before final conversion if further editing is required.