It seems to be a direct measurement, not derived from anything. You might be able to derive WBT given the dew point and dry bulb temperature, but it would still need units like C or F.
Perhaps you were thinking of a different measurement?
A measurement that has no unit is relative humidity. It is just a percentage. There is no way to measure relative humidity directly and get any other type of unit besides a percentage. Instruments that measure relative humidity directly measure in percentages.
edit: ah, you can use C2 = Celsius*2 whether you're talking about regular temperature or WBT. C2 is the 'derived' unit. Not WBT.
Yes you can use C2, but why not just use F which still has better precision than C2[1]? For low values of C2, you may confuse it with plain C...
[1]: https://uxdesign.cc/celsius-needs-a-redesign-41709e048c4a