SpiderLegs wrote:the hiking shoes I have are low cut and not that much beefier than running shoes
When you say "low cut", I gather that you mean that the shoe offers little or no ankle support.
The shoes I mentioned earlier are like that too, but also have a very low "stack height". I.e. there's little to no cushioning or other material between your foot and the ground. Some of the shoes that I'm wearing have a 5mm Vibram sole with only a couple of thin layers of leather above the rubber sole. So, total stack height is probably about 7mm.
By way of contrast, the Altra Lone Peak 3.5, which Altra considers to be a medium cushioned shoe, has a 25mm stack height. This means that the soles of your feet are close to an inch off the ground. Altra also makes the Olympus which has 36mm stack height! Since your feet are higher off the ground, the potential for rolling your ankle is much higher in this type of shoe.
The down side with wearing a minimalist, low stack height shoe is that there's not much support for your feet. You'll also feel many of the irregularities of the terrain including roots and stones. Many of the minimalist shoes don't have very tough soles allowing for easy thorn penetration - most of them are very bad in this respect, but there are a few good ones.
Anyway, assuming you're not already wearing a shoe with a low stack height, that may be something to consider too, especially for shorter hikes and/or training hikes.