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Uausally this is not a problem because most spinners come with a backplate hole that is too big and sleeves in different diameters are provided to take up the slack.
You could use a tapered reamer or as I prefer, a "Unibit" stepped drill bit, they come in 3 sizes and each bit has 8 sizes on it depending on ones needs.
The tapered reamer would be the easier of the two because you can hold the plate by hand.