The aircraft is normally weighed on the ground flaps up, gear down (the latter is pretty much essential!). Last I looked the flaps and slats were not retracted for take-off, so the function of safe windspeed to take-off or stall speed is far from clear.
The shape of the aircraft, any aircraft, will be such that the wind vector (as well as the scalar) will affect Cl and Cd on the ground (since the drag effects will act about a CG will above the undercarriage, that skew things as well). I'm afraid that you are probably being badly misled by the grossly simplistic explanations of aerodynamics used when training pilots.
You are never going to routinely find a spot, on any major airport that I've visited, where you can guarantee no significant 3D wind effects - in particular rotor over buildings, vehicles, trees, that hill over there.... This will all throw the results.
So, basically the enormous degree of uncertainty over both the actual 3d wind model around an aircraft on the ground, and the effects of that airflow pattern - which is infinitely variable - will have on the complex 3D shape of any aircraft - and then the resultant forces on the aircraft make accurate weighing of an aircraft outdoors, at an airport, a virtual impossibility.
Weigh the aeroplane by all means, but the only way you'll do it reliably is in a hangar or that great rarity, perfectly still conditions.
I'm afraid 'though, I remain of the opinion that the big issue is documentation control.
G