Not sure how to call this, there's similar named questions in blender but those are far from what I am trying to do.
What I want & what I have
An edge loop that has equal distance to target object's edges (Black part in below image)
Could manage to make sharper one via Mesh Tools > Offset Edges
Answers I've tried
Is there way to make this work?
Even if it only works in 3D mesh (aka shell around entire object) that would be totally fine with me!
Currently I'm just performing bevel manually in 2-step as a workaround.
Edit
Below answer worked great! Managed to 3D print badge that doesn't hurt user!