Welcome to the forum!
The swift will likely be 5500-6000 lbs loaded. A gear change may help some with perceived performance but that is not all there is to pulling... Now to your safety question.....what do you mean by safety?
The safety of the drivetrain? Or your personal safety?
That truck will be able to pull that trailer around at 55-60 mph on the interstate. So your personal safety really depends on you as a driver. The truck is up to the task here.
Now the safety of the drivetrain.... The motor will be fine. 3.73 gears put you in the 7000 lb tow rating range. It will have to spin at higher RPM's but that's fine. The transmission is the weak link. I would put the biggest Derale or B&M transmission cooler on it I could find. Keep the tires aired up to max psi, use a WD hitch and sway control, and use a good brake controller.
Question...why not consider the Jayco Jay flight 26bh? The weights are similar but you get heavier duty axles, bigger fresh water capacity and nicer cabinetry. The price is only a few thousand difference as well. Same basic floor plan.
Thanks