How to implent movement AROUND grid

Hello,
Everyone seems to be asking about how to implemnt gridbased movement, where you move form tile to tile.
I on the other hand, need to find a way to move on the edges of the grid only (around the tiles). How do I do that?
I was thinking about adding colliders to the tiles so the character can only move between the tiles, but it seems like an odd option to me.

Based on the information you give i would say this is completely a presentation problem.

The movement is exactly the same in both cases. The only thing that changes is how the visible grid is positioned in relation to whatever is moving.

Put a chess piece in the middle of a square. If you move it the length of one square you will always land int he middle of another square.

Do the same but put the piece in the intersection of 4 tiles and do the same and you’ll always land in another intersection

If your game mechanics allow you to get by using only a grid, the benefit is exactly the fact that you don’t need to fiddle around with physics and sacrifice the performance for it or deal with randomness in movement and positioning.