We experience very little if any sway with a TV/TT combo that is very similar to the towing combo you asked about. With a good quality WD/SC hitch that has been properly dialed in, along with proper inflation of TV and TT tires, TT sway should not be an issue. Make sure that tongue weight is in the 15% range and you should be good to go.
We've been towing our 10K TT with our Chevy HD gasser for 7 years and enjoy very comfortable tow, even on windier days at interstate speeds. I have passed many a TT being towed by 1 ton trucks, some even duallys that have exhibited lots of sway. Also pass many sizable TTs being towed by newer half ton trucks that appear very stable going down the freeway, as one can see it isn't as simple as getting a huge truck to solve sway issues.