I'm still pretty new to Blender and 3d modeling in general so I probably don't have the right vocabulary to describe exactly what I'm trying to do, but I hope the question is clear enough.
What I need is to scale a mesh evenly but without creating intersecting geometry as shrink/fatten tool does. In other words I want the scaled mesh to fit neatly inside/outside of the original unscaled one.
As you can see the duplicate mesh that is simply scaled along the axes naturally doesn't fit inside the bigger one at all, and the one edited with the shrink tool while being kind of closer to what I want intersects both on itself and with the original mesh.
I've been stuck with this for a while now and would be grateful for any tips you can provide.