A micrometer would be your best bet, then add .001" for a slight bit of additional play. This also facilitates lifting the protractor off the table without cracking it (it is glass). Too tight, and there's always a chance...
Agree with Richard. Even if you knew the spec, your spindle might deviate. Any deviation toward too large would make the Mint unuseable.
When measuring, take multiple readings along different axes of the spindle, in case it has any irregularities. Add .001" to the largest confirmed measurement.
The vast majority of LP's have more "slop" on the spindle than the Mint will, so a "perfect" fit is overkill, as well as increasing the risk Richard mentioned (which has already happened to at least one fellow A'goner).
I think it is better to get a digital caliper and measure the spindle. Even if the manufacturer specifies the spindle diameter, this measurement is often times rounded up. Digital calipers go from about $30 and up.
For the Mint tractor, it is better to have the exact spindle diameter to 1/10 or 1/100 of a millimeter. This is one of the main reasons why the Mint tractor is so accurate.