I would use a WDH along with sway control. A basic round bar WDH along with an add-on friction bar should be more than adequate if only doing mostly 20-50 mile trips. You could go to up to something like an Equal-i-zer or Reese dual cam WDH but not necessary. The Reese can be finicky to set up too.
Specs. for a 2014 model Skyline are
here. I assume 2015 would be pretty much the same. Hitch weight is listed as 425 lbs. That is dry tongue weight and with the TT fully loaded for camping, it *could* end up around 500 - 600 lbs, hard to say. Factory dry weights always go up - sometimes a little, sometimes a lot. The Skyline is 20' long and single axle. Relatively light for that length of TT.
The first thing I would do is figure out what the actual tongue weight is so you have a real number to base a decision on. You can go to a scale (Cat, commercial highway, grain elevator, etc.), use the bathroom scale method or buy/borrow a tongue weight scale. If going to a scale, you will need 3 separate passes and if you want to do this, look up how to do it or ask here. If at a scale, you might as well determine your actual payload capacity at the same time for the record.
While your truck may technically be plenty fine on payload capacity, I would measure the fender heights before hooking up and after and see how much rise there is on the front. For a '97 truck, I doubt the manufacturer will say how much weight to restore back onto the steer axle. I *think* the thing to do in that case is to refer to what the WDH manual says, but you won't have a WDH at this point. So I think the thing to do would be to restore the front fender height to what is was unloaded or maybe within 1/4"? Someone here with an older truck may say what's good.
You'll have 500-600 lbs cantilevering on the ball out the back and it will remove some amount of weight off the steer axle. Depending on how much the front rises (without a WDH), it may negatively affect handling and safety. I think that's the important thing to consider, not whether your truck can handle the payload or not.
Check the receiver rating on the truck (if you have any idea what it could be). Receivers normally have a max. tongue weight with no WDH and another (higher) number if using a WDH.
Even if you could get away without a WDH, I would use one so you can have sway control. You could find that driving in windy conditions or when passed by semis on the highway it's a real handful. It's the frontal and side area of the TT that will affect sway and handling and get you, not the GVW of the TT.
As a personal experience comparison, our first TT was a 20 footer (5K fully loaded for camping). We towed it with an F150 that had a V6 (205 HP). We did not have CC and I had trouble maintaining a steady speed in strong headwinds or sidewinds from the constant buffeting/gusting and it was very difficult at times to maintain a smooth/steady straight line. I could manage big passing trucks at highway speeds and it was a bit of a handful sometimes but strong winds was not fun at all. If we had kept that TT & truck, I most definitely would have added sway control.
FWIW, you may find adding HD shocks to the truck will help handling a lot (we did that on our F150) and it sounds like you keep it in good shape, but unless you know for certain it's all good, check the front end for wear and play (considering it's a '94).
JMHO...