I would spit out HTML that gives the grid, and then a list of words. Each word is wrapped in a JavaScript link that calls a function which clears existing markings, then proceeds to color the letters in such a way that it is obvious what order the letters make that word.

One way to do that would be to have multiple arrows which can be set as a background, and set all of the classes of the table cells appropriately to make the right background images show in the right places.