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Carbide will do it and you can probably make do with a carbide tipped masonry drill from your local hardware store. It will make an ugly, sloppy hole but it should make one.
The correct drill for your problem is called a straight flute carbide drill. They would go through that tang like it was made of butter and the hole would be clean, straight, and the nominal size of the drill you selected. They are pricey and only available from machine supply shops like MSC but they make short work of that problem (which we all have sooner or later) ...
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