Will mechanical blending denature alpha amylase / glucoamylase?
There are three ways in which a protein can be denatured:

Chemically (for example, the 'cooking' of protein like fish by acid, as in ceviche).
Through heat.
Through mechanical force.

I will assume that in your situation, chemical denaturation does not occur.
From a quick search through some scientific literature, mechanical protein denaturation is a fairly new research topic. I found an MSc thesis that lists three experimental techniques for mechanical denaturation: optical tweezers, magnetic tweezers, and force mode AFM (atomic force microscopy). All these methods act on a single protein molecule, grabbing it at two ends and 'stretching' it, which denatures the protein.
While it is possible that your stick blender denatures some proteins mechanically, but it seems unlikely to have a large effect. It seems much more likely that the blending is causing your mixture to heat up above the denaturation temperature through friction. This could also explain your inconsistent results, if you do not always reach this temperature.
A good test is given in mbjb's comment: blend the oats first, let the mixture cool down if it has warmed up, then gently mix in the amylase. You could measure the mixture's temperature throughout the process if you want more information, potentially comparing it to amylase's denaturation temperature (which I could not quickly find, but you might be able to).
PS. in response to your comment: the enzyme reaction process will be sped up by temperature (where warmer means faster, until you get to the denaturation regime) and proper mixing. I see no other mechanical advantages of blending in the amylase using a stick blender.