Youre going to get a lot of opinions on this. Yes, that's a lot of truck for the trailer, and techincally by the numbers you should be fine towing with or without a WD hitch.
As far as sway, a sway event that crops up as the perfect storm will toss your truck like a 1/2 ton if it hits you right. I've seen one in person and I'm here to tell you, you're along for the ride, and that's all. Best to be prepared when that day comes, that's my .02.
"It`s not important that you know all the answers, it`s only important to know where to get all the answers" Arone Kleamyck
"...An unarmed man can only flee from evil, and evil is not overcome by fleeing from it." Col. Jeff Cooper
Sunset Creek 298 BH