Assuming the clamps & hardware haven't changed recently, I think you can use standard, commonly available 10-24 screws for the clamp.
I have a couple of older Lansky sets and replaced the stock screws in the clamps with longer ones of the 10-24 type to accommodate thicker blades. You might also consider getting replacements in brass instead of steel. The softer brass screws are less likely to damage the threads in the aluminum clamp if they're overtightened. If your screws aren't tightening the clamp effectively, you might check to be sure the clamp's threads aren't stripped or otherwise damaged. If they are, it may be simpler to just order a new clamp and then consider using the brass screws to protect it. The clamps aren't very expensive - I'm seeing them priced at around $13 - $14 online.
I found all the screws I needed at the home center (Home Depot / Lowe's). They're a very common size and should be easy to find at most any hardware store.