My 9-year-old daughter and I hiked up the Narrows about 45 minutes (after the end of the trail) and returned to the car. It is about 70% walking in ankle- to calf-deep water if you pick the right route, the remaining 30% is river bank and sand/gravel bars. There are deeper spots, some MUCH deeper, and that might be inviting by mid-summer, but I found it easier to avoid those.
In mid March, flow was low (55-60 cfs) but cold (40F). It was late in the day with no direct sunlight and due to the early season, the rocks weren't radiating heat from prior sun exposure. We used fleece or thicker Smartwool socks inside of low-cut hiking shoes or secure water shoes. With those cold temps, neoprene socks would have been better and neoprene wetsuit booties would have been ideal, but the wool socks sufficed for our shorter trip. My daughter had a shortie wet suit over a rash guard long-sleeve top and a expedition-weight polypro bottoms (which made for an okay wetsuit bottom, not as good as snug fitting neoprene, but we had it and it fit well). I wore shorts, two light shirts, and a fleece pullover.
We didn't use hiking sticks, but I held her hand in faster-current stretches. On my own, one or two trekking poles would have let me go faster. With her, I wanted one of my hands free to hold one hand of hers.
The rental gear that virtually everyone else had on looked odd - pretty clunky footwear, drysuits that seemed overkill, even in late Winter (everyone had them mostly unzipped, so they wouldn't have been very dry, if they fell), and the poles weren't Black Diamond Trekking Poles. They were a six-foot length of wooden closet rod with a strap attached. Sure, it worked, (and lack of any basket is a GOOD thing among the rocks and cobbles) but, heck, buy a beater broom at Goodwill and saw the handle off - it will be lighter yet plenty strong enough. Some of the renters looked a little sheepish in their over-kill gear as a little girl and a guy in shorts went by. (Disclaimer: it was a little girl whose school insists on "outside recess" down to -10F, so she's not a temperature weenie).
A great way to fine-tune your gear: before the leaving the parking area (oh, yeah, you'll be there when there's no private vehicle access) is to eyeball what the people returning are wearing and ask if their gear was too much, too little or just right.
I find that my shoes clean up pretty well. Most shoes do if you just run them through the laundry with any modern detergent. Then a low-heat drier or just air dry them (as Alaskans, we have lots of Peet Shoe Dryers around, but you probably don't).
Here's Phoebe heading upstream last month: