Green areas on the normal map

Hello Blender community :slight_smile: , aspiring creator here.
I am having troubles with baking a normal map.
Neither various ray distance values nor cage method work for me.
My guess is that the green areas refer to places where the mesh is too close to itself thus rays are hitting back.

  1. Is there a way to make it work without retopologizing the object?
  2. Should I always be concerned about green areas?
  3. Or perhaps I have to (but would not like to as it is tedious and we are all lazy by default :smiley:) set up a cage with godly precision?

Here is the blend file with the current status:

Edit: Here is a picture with the areas I am worried about.

Thank You in advance :slight_smile:
PS. I used smart UV project to unwrap the mesh