If the setup is balanced correctly etc, you have not taken as noted, too much weight off the FA, you should NOT NEED a WD or sway control. If you do not.....as noted, all bets are off. I've had an unbalanced equipment trailer that weighed 8500 lbs, with ALL of the wt on the axels, no hitch wt, dang near take a 12K empty dumptruck off the road with a 26K gvwr and 35K gcwr. I've seen a tandem dually Kenworth, with a swaying flatbed incorrectly loaded fore and aft wise. I've seen a 5W behind one of the supposedly can do no wrong Dogde fummins things swaying away!
BUT, as noted by many, you SHOULD be able with a ball or pintle mounted trailer pull upwards of 60-65 in any condition with out sway etc IF it is setup correctly. I have gone thru 50 mph side winds with my old TT in the Columbia river gorge without issues. Yeah the whole rig went sideways, rocked side to side with the higher gusts, But even with a dual cam in similar situations, I felt the wind. Altho a WD only, feels the wind less than nothing, and a dual cam is better than a WD only.
Marty