Some observations from that paper:
Notice their equipment list includes a sonic anemometer (Vaisala WS425). This was used to collect wind speed data simultaneously with other measurements.
Equation (11) defines the independent variable in their "curve fit" to the errors that could correct for solar errors. So, to make these corrections, you must compute "X" from their equation (11).
In the numerator of (11), we have "Rad" which is shortwave radiation in Watts/sq-meter. You may have a sensor that can do that...although I don't think OS offers such a sensor (I know they have a UV sensor but that's not what you'd want here). And it probably does not need to be all that accurate (a few numeric examples would prove or disprove this).
The denominator of (11) includes two constants (rho and C-sub-p), the thermistor temperature and "U" -- the wind speed. This might be a problem. Since "U" is in the denominator, if it ever goes to zero, then "X" goes to infinity and their curve fit no longer works. At a minimum you would need to place an OS anemometer at about the same location as the shield solely for the purpose of measuring "U". I'm fairly certain that if you used an anemometer at a different height (like 10 or 30ft AGL), these corrections would not work.
Then if "U" gets too small you would need to "cap" it at some safe limit so "X" does not blow up on you. As mentioned above, since your anemometer of record is either 10ft or 30ft AGL, this anemometer is a separate unit -- you don't get to make double-use of your anemometer-of-record. Now you need a weather station that can process readings from two anemometers.
Finally, I've not worked through the numbers, but there will be some minimum wind speed you need to discern for the corrections to be accurate (the "cap") -- I don't know what that is or if the OS anemometer can read a wind that slow (I'd give even odds on that one). The Vaisala sonic anemometer is capable of measuring very low wind speeds more accurately than the OS unit...you'd have to work through some numeric examples to figure out if it really matters or not.
The night-time corrections they show are based on "net radiation" instead of shortwave radiation which would require yet another sensor...however, they are so small that you could just skip that part.
So yes, this might be do-able, but it sure seems like it would be less expensive and less work to purchase a fan-aspirated shield instead.