Thanks for the advice.
I might try the insole solution, however for running shoes I gave it a try already and I don't believe much in it. It's about the whole shoe construction, not the only sole, at least for running.
For hiking probably the insoles make more sense, perhaps this is why there is no single range of products that include pronation.
However for my case, the high mountain boots I have are close to their end of life (worse, the more I use them the smallest they feel ! I can't explain that) so this is why I am looking for a whole mountaineering boot.
The low hiking boots which I use mainly for day hikes on maintained trails are quite new, what's more I use in them insoles initially bought for the running shoes (ironman gel insoles, far too heavy for running but great for walking)
I just had a look at the thread about trail-running shoes with rubber soles
, the La Sportiva sound fine, but these are rather low shoes like I have.
I might go to some specialized shop where someone competent recommend me a proper boot after analyzing my feet.