With that sized truck, you might get away without 1. But if it were me, I would still use 1.
That Shamrock has a listed tongue weight of 565 lbs.....about the same for my SV 263. Loaded for camping, my tongue weight is around 700 lbs. Without a WDH, that weight takes about 300 lbs. off my front axle, and adds 1000 lbs. to the back axle. A 2500 should be able to handle that weight OK, but you will be upsetting the balance of the truck somewhat by taking that weight off of the front axle. I betcha without a WDH the back of the truck will sag some.
Another item if you decide to pull without a WDH is the hitch rating. On my F150, the hitch is rated for 500 lbs. weight carrying tongue weight, but add a WDH and it is rated for 990 lbs. If you decide to tow your trailer without a WDH, make sure the hitch is rated to carry the tongue weight of your Shamrock.
Even with a 24 foot trailer, I would still recommend some type of anti-sway system. Even with a heavy truck like yours, the wind can still push you around.
Your total towing experience will probably be much better if you use a WDH and a sway system.
Chap , DW Joy, and Fur Baby Sango
2006 Ford F150 Super Cab 4x4
2008 Surveyor 263