'tain't easy
Whenever I have tried pulling my yaks down steps I have found that the cart, if not strapped on, has a tendency to drop out of the scupper holes when the boat spans a step and the gap between the hull and the ground gets beyond a certain distance.
This can be quite catastrophic if you are on a steep slope with a heavily-laden kayak because, while the kayak may be supported upright when on the cart, as soon as you remove the cart's lateral resistance and let the yak rest on its nose, tail or bottom, which aren't flat, it WILL fall over in one direction or the other and stuff that is stowed but not fixed down will slide about and exacerbate the lean. In some cases the kayak will flip right over on the slope and snap fishing rods that are placed in the holders (do you detect a tone of heard-earned experience in this reply?)
On a steep-enough slope, if you do not have someone with you to help, as soon as you let go of it to set it back on its wheels the boat will then slide off down the slope/stairs/steps/dune and I have experienced the kayak falling off its cart and then, because of the slipperiness of the hull on the grass it fell onto, sliding down the slope on top of me and being impossible to stop via the front towing handle because of its weight: I just had to step out of the way & let it find its own way down.
My recommendation: carry it down if you can (I would require assistance with my Oasis), if not, then a strapped-on cart of one sort or another and push the kayak down the stairs/slope. I usually try to avoid stairs and instead lower the kayak down a nearby slope (if there is one). If there isn't one and/or the slope is very steep I would definitely consider trying sliding the boat down whatever surface without a cart - I usually have sand/dunegrass but the poly hulls are incredibly tough so it is unlikely to sustain fatal damage even on harder surfaces like wood (though I agree that rock/concrete/gravel would have me wincing a bit) - I would only do this with the boat unladen, though, and then I would load it up at the bottom of the slope.