Short answer: NO
Are you sure your truck is limited to 500# tongue weight? Likely that limit is if not using a WDH like on many class 3 hitch receivers. Most are marked 500 tongue weight/5000 tow weight. For with a WDH, the limits are much higher.
Your weights are well under the most basic optioned recent F150 towing capacities.
The only reason I see to get a WDH would be to use one with integrated sway control for a tall wind grabbing trailer. That said, I'm using the WDH I used with my 4K# TT on my 2008 Explorer on my 2029 F150 V8 super crew with standard towing package. I've towed the TT without the WDH but I'm much more confident in the crosswinds at interstate speeds with the WDH.
Did you lookup your truck using the Ford Towing guide for that year? Most are available online and will list your factory towing and load limits based on wheelbase, engine, rear axle ratio, and other factory options.
2019 Wolf Pup 16 BHS Limited, axle flipped
2019 F150 4x4 SCrew SB STX 5.0 3.55 factory tow package, 7000#GVWR, 1990 CC Tow mirrors, ITBC, SumoSprings,