I've hiked the Narrows three times from the top down as a day hike, and at least seven times from the bottom up. My first trip I used hiking boots and hiking poles. It was doable, but the next and all subsequent times I rented the boots, socks and wooden stick from Zion Adventure Co. It is unbelievably easier with their equipment. The single wooden stick is sturdy to hold up between the rocks, and you can really dig in and get good leverage. Hiking pokes are more likely to skid across the rocks and are susceptible to bending and breaking, especially at the pole joints. And the shoes...they are perfect for the Narrows. They stick to the slippery rocks much better than my boots. Personally I wouldn't wear the shoes without the neoprene socks, they fit together. There is a great deal of pounding on your toes and feet, and the socks are extra cushioning. It would be like wearing hiking boots without socks.
That said, the Virgin river is very low this season and navigating through the water will be easier than the norm. If you want to avoid the rental expense and use your regular hiking equipment, this is the optimal time to do it.