The shim goes between the bearings inner races, so a thinner shim would reduce end-float.
Best, and more accurate, is to remove the hub from the car and measure play on the bench with a dial micrometer, no fancy tools needed.
As you need to remove the shaft from the hub to change/adjust the shim, I would invest in a set of new bearings as well.
As others mentioned, new bearings might bring the end-float to spec with the existing shim.
But again, being tapered bearings, I would recommend setting them at zero to a slight pre-load.
You can easily measure preload with the help of a luggage scale.
https://parts.jaguarlandroverclassic.com/parts/index/part/id/898.1457.4789.21504/brand/jaguar/