Mike -- Yes, you should be able to wire it as you have described. It's not complicated and there aren't any weird/obscure things about it. If the axles are modern Dexters and all three have brakes, you should have few issues with that rig. Just go easy on the controller the first test. With all three axles braking, you'll lock them up on even a light setting. So start at zero and slowly work up until you find the happy place. We don't want you getting flat spots in those tires!
Also ... try to avoid hauling an empty trailer with a loaded truck. If you have to, then be sure you adjust the brakes way down or you'll lock 'em up, make lots of smoke, create a big stink of burning rubber which will cause all the other drivers to look at you and think "What a doofus." I know a guy who did that once ...

Happy Hauling!
And as long as we're trying to save your tires ... You *did* check that 2-inch recycled concrete for little pieces of rebar, yes? Or is that big marble chunks?