If your "sway bars" are like this, then go ahead and set them up for the new truck.. This is a "Weight Distribution" setup which puts weight back on the front axle and makes the whole rig tow much better..

If your "sway bar" is a thing that you attach to the little ball on the hitch and to the trailer and then crank down on the handle, you probably don't need it, but it won't hurt anything either..
Both systems help with towing, but once a trailer starts to really "sway", that's when the new F150's "sway control" will kick in and try to stop it. It does not prevent it.. That's what the bolt on and WD setups try to do.
My TT is #5000 soaking wet, but I use the WD setup in the pic because I have over #650 tongue weight and that does sag the rear end a tad.. Put the bars on and it's back to normal height and weight is put back to the front, so it tows just fine.
good luck!
Mitch