I don't see why sodium iodide wouldn't work for that purpose. All you would need is the iodide ion to get your iodine in solution, right? So just
replace KOH with NaOH and you should be good to go.
Or if you really need the KOH, I suppose you could try to synthesize it using other potassium salts that might be more readily available. For example,
the wiki lists this as the historical method of preparing it:
Ca(OH)2 + K2CO3 --> CaCO3 (s) + 2KOH (aq) |