You need to set up the WDH based on front wheel loading (aka height).
With trailer removed, measure the height of the front wheel well.
Add trailer and engage WDH. Front wheel well measurement should be as close to previous measurement as possible, but you typically do not want it be be lower than stock, unless you know you have plenty of front GAWR capacity.
This setup will ensure that you have proper stability during steering, braking, etc. And it will leave the proper amount of loading on the rear.
To answer your question, I would say "yes", it's possible that too much weight transfer could cause sway, if it's to the point that your rear axle loading is lighter than stock. But in that case, you would be seriously overloading the front wheels, which you would recognize with your measurements.
thebrakeman ('70), DW ('71), DD ('99), DD ('01), DD ('05)
2004 Surveyor SV261T (UltraLite Bunkhouse Hybrid)
2006 Mercury Mountaineer V8 AWD Premier
Equal-i-zer WDH (10k), Prodigy Brake Controller