How to use AppleScript to un-hide a file's extension?
Never mind! I found the answer here:

Super User: Show/hide extension of a file through OS X command line

I will delete this question now!

EDIT - 

Since some are upvoting this question, I will echo the top answer in the linked question (supplied by @slhck).

A straightforward solution exists, because AppleScript specifically offers a set extension hidden command designed to do exactly what I'm looking for.

tell application "Finder"
    set some_file to (choose file)
    set extension hidden of some_file to false
end tell


And that will make the file extension visible!