I would work on strengthening your ankles v.s. wearing braces. Calf raises etc.

I hiked up to trail camp in my Altra Lone Peaks. I switched to the Altras after using light(ish) weight boots (Merrels etc). I've done multiple overnight backpacking trips with them. I much prefer the Lone Peaks- although I wish the soles last a bit longer. If I was rock climbing or bouldering, maybe I'd pick something with a sturdier sole.

I purchased a pair of La Sportiva Bushidas to try to get a longer lasting sole and have only been marginally happy with them v.s. the Lone Peaks.

I don't believe any boot short of a ski boot could provide enough ankle support without tying it so tight you'd be miserable.