Detecting what surface character is moving on and restrict movement outside

I'm trying to make a game where you can switch between flying around in a spaceship and walking around inside it with a click of a button. The ship's bridge, that you walk around inside, is a window that pops up in front of the spaceship. Everything in the background gets paused with 'timescale = 0', and I create my own timescale to make my ship commander character move. Problem is that colliders use the timescale, so they won't work, so I'm looking for a new way to restrict the ship commander's movement to inside the ship.

Is there a clever way to check which type of surface type the character is moving around on? Maybe by checking for tags on the texture the character is touching?