Being old enough to remember such suitcases, on cheaper ones (usually cardboard, not leather) the key is usually a simple pressed steel (about 1.5mm thick) affair with a little peg sticking out one side – i.e. it is no more than a simple lever to turn the lock. Some suitcases do have slightly more sophisticated keys, but the thickness of that lock suggests only a single lever.
I threw away a set of suitcase locks and keys of similar type a few months ago…
Neil