If the holes are all the same size pop in loc-tites that all have the same outer diameter buy the insides comes in various sizes. Print your labels to fit inside them.
That's an interesting old cabinet to use for your collection. Antique dental cabinets and library card files can also be adapted for this purpose - good luck in your search
I have one of these, likely from the same manufacturer (it looks identical). Our local library built a new building some 10 or more years ago and they sold off all the 'undesirable' surplus. The old card catalogs were part of that. My father in law bought a few of them, gave me one. He paid $15 per unit! Unfortunately my unit is missing the upper portion (the pull out shelves and top) so I have never done anything with it. I cant bear to toss it or otherwise dispose. Its too interesting. But what will I do with it???
Round labels designed for coin cabinets can be bought from Spinks - mail order from their web site www.spink.com