Top-down 2D - crawling script

Hi,

Quick disclaimer - I am new to Unity but love it and am eager to learn. For practice I'm working on top-down, Metal Gear Solid-like game, where Player character can stick to walls and crawl under some obstacles.

I wonder, how, using 2D Unity physics, can I allow those actions. My idea would be disabling some tagged group of colliders on walls etc. to crawl under them? I also wonder how to check if player is by a wall that he can press himself to. Use triggers on each applicable side of an object?

Please let me know about any solutions that come into your head, I would be extremely thankful for feedback and will definitely try as many approaches as I can.