I think that I will be proven wrong, but for the first repetition you could add a solution containing iodide ions, but not sodium ions, for example potassium iodide. This should still catalyse the reaction. Then, for the second repetition, add a solution containing sodium ions but not iodide ions, e.g. sodium chloride/sodium hydroxide. This reaction should be slower. Hence, only the reaction with potassium iodide was faster, proving that the iodide ions, not the sodium ions, acted as a catalyst.
You could potentially also just use the sodium iodide for the first repetition, then sodium chloride/hydroxide for the second, as this should achieve the same result.
I hope this helps, and if anyone else comes across this thread, feel free to correct me!