Don't worry about changing the tongue weight when using the Andersen hitch (or any hitch for that matter) as the hitch does nothing to change tongue weight. It only changes the amount of weight that the truck sees.
The tongue weight, and therefore the tendency of the trailer to sway or not, is the same whether a WD hitch is used or not. The only way to change the tongue weight, and possibly affect stability, is to move weight around in the trailer in front of or behind the axles, change the tongue length, or move the axles themselves.
Barney