For various reasons, I'd personally get him hiking boots. (Please don't take this as a personal attack btw, obviously do whatever you want!)
One, the ankle support on a boot can make all the difference to avoiding a twisted ankle on uneven terrain.
Two, the waterproofing on a boot will keep the feet dry. Even if it doesn't rain, there's always the chance of a slip or step into a hidden water source on a long hike and ending up with a wet foot for hours.
I'd also recommend the two-layer hiking socks you can buy, the layers rub against each other rather than the skin and are a lifesaver. I've done a lot of volunteer work which has required being days in a field for festivals etc, and I swear by the socks. I bought my DS a few pairs for his DoE bronze and he got on with them.
We walk absolutely loads as a family as well so we aren't sedentary. DS took his lightweight trainers as something to change into when they were at camp, but he did have time to practice with the hiking boots we bought him in advance.
I think there are loads of options out there for hiking boots/shoes and they're worth having a look at. Also you don't need to spend loads to have decent ones, imo.