Most cargo trailers don't get a WDH. This is for the typical length, maybe not more than 12' length and no more than 6'6" tall. The longer/taller it gets, the more likely it is to catch the wind. The 6' wide, 6'6" tall, 12' long enclosed dual axle trailer I towed, pulled great without any sway control. There were a few times that it would have helped to have some weight distribution though.

When it comes to bumper pull trailers, you can always use a WDH. Sometimes overkill is OK.

 

No idea of weight. I’ve hauled 17K in that box before without issue..

WDH is not necessary on the 12’.
The 26’ definitely needs a weight distribution hitch. Tongue weight can get the rear of the truck sagging..even my prior F-350 DRW.
With a WDH, it will run dead level, and that’s a must if your trailer uses Torsion axles and you want your tires to stay intact..

 

In 2004 my parents got a $30,000 quote to move 300 miles. My dad couldn’t stomach it and bought the below trailer and he and I hauled weekend loads for a summer. I don’t think my parents could have moved any faster - a lifetime of stuff was easier to go through one trailer at a time. I’m still not sure why I had to move 5.25” floppy disks or bankers boxes labeled “Enron”... but at a lot of other stuff did get filtered out in the process.

So, speaking as someone who has done what you’re thinking:
1) as usual everything y2kw57 says is spot on. Be weary of ununiform loading. I liked to plan for dense stuff around the trailer axles and infill from there with lighter furniture. The front and rear ramps on the v nose made a lot of sense
2) weights - I think 10k or two 5200lb axles is a good goal. The trailer below is 3500lb axles. We were routinely on the edge
3) yeah yeah... fuel goes up, your time is valuable. But a retirement move like my parents is tough. You’ve got a lot of stuff to go through. If you have the luxury of taking a couple months and not being in a crunch packing your loads, take it.
4) 17 years later I’m still using that trailer my dad bought to move.... every once and a while he asks me when he’s getting it back...

 

I use my 8.5 x 20 SuperCoach Race Trailer to haul whatever I need. It weighs 3790 empty and the GVWR is 9990. Not sure if this is something you would consider but it has worked well for me for 5+ years now.