Look at the sticker on the aft-facing portion of your factory hitch receiver. It's too cold for me to go look at mine right now, but if IIRC, its maximum is 500 lbs tongue weight and 5,000 pound trailer weight without a weight distributing hitch. If that's the case, yes, you need weight-distributing for the 25' Safari.
Have you ever watched cops in a much lighter Crown Vic turn a much larger, heavier vehicle sideways by giving them a push on the rear bumper? Yes, you need sway control.
Lower, rounded Airstreams are a little less susceptible to crosswinds, but like any trailer, they can sway. Bigger, heavier trucks are less likely to be affected by sway, but they certainly can be.