I didn't see where the OP said the trailer had no brakes. IMO that would be a deal breaker even with a pickup. I find it impossible to believe the trailer for a boat that large wouldn't have them. I *think* the threshold in OR where brakes are required is 2,000#.
Charlie is also right about how the weight can add up more than you think. Is that 3400# figure based on weighing it at a weigh station ?
As far as sway goes, Charlie is again correct about going too fast, but the last thing you want to do in that situation is hit the tow vehicle brakes and lose your rolling traction. What you need to do is one or both of 1) apply braking to the trailer using the brake control actuator, 2) apply forward power with the tow vehicle so you have a force vector going straight ahead. Then get off the gas right away and let the whole thing slow down.
Obviously you can only do this with electric brakes and a controller; if this is just surge brakes on the trailer you really don't have the same level of control.
I would also say to consider the relative weight of the tow vehicle compared to the trailer. If you are pulling more than the tow vehicle itself weighs, you need MORE braking on the trailer.
Finally, there's a big difference between having enough power to tow on flat ground and typical road grades, versus a steep, wet and slick boat ramp. Something to consider.
tl;dr version:
Assuming you have the tow rating to do this, and electric brakes, and can set the controller brake force on the high side to account for weight ratios, and keep it to 55 or below, yeah you probably can do it.