How do you get an angle of a point on a collider?

Hi guys,

I'm new in Unity/C# and have a problem with properly placing "player" which is game object and box 2d collider on edge collider surface. The idea is that user swipes left/right and "player" smoothly slides left/right directions.
Here is an illustration I made which describes the problem above:


P.S. I would like to avoid using of physics if possible.

Thank you, in advance.