Searching for Pickaxe on the Nexus, I only found model replacers (Minecraft Pickaxe, Lego Pickaxe, etc.) or tweaks of the normal pickaxe. Nothing to allow the AN Pickaxe to work on non-Stahlrim mines.
This is because the Ancient Nord Pickaxe is supposed to be the only one that mines Stahlrim and that is all that it is used for.
However, you can do this mod yourself. Just open up the editor and change it's type. Note, I would not mess with the stock in game one, but clone it, create a new ID, change it's type and then you can have your axe for mining other things. Unless of course, there is a limitation where the Stahlrim requires a certain axe to mine, then we are right back at my first sentence.