Wall running using raycasting.

Hey I need help getting my player to snap to a certain place, that is like 1 unit away from the wall he is next to, while he is off the ground.

Here is my code:

 using UnityEngine;
 using System.Collections;
  
 public class TP_Raycast : MonoBehaviour
 {
     public static TP_Raycast Instance; 
     
         //Creates a ray
         private Ray ray;
         
         //Creates a RaycastHit
         private RaycastHit hit = new RaycastHit();
      
         //Get this GameObject's transform
         private Transform playerTrans;
      
         void Awake()
         {
             //get this Transform
             playerTrans = this.GetComponent<Transform>();
         }
      
         // Update is called once per frame
         void Update ()
         {
             //Ray to the left of player
             //recreate the ray every frame AND draw debug line for the ray
             ray = new Ray(playerTrans.position, transform.TransformDirection(Vector3.left));
             Debug.DrawRay(transform.position, transform.TransformDirection(Vector3.left), Color.green);
              
             //Casts a ray to see if something has hit it
             if(Physics.Raycast(ray.origin, ray.direction, out hit, 1))
             {
                 //Collision has happened, print the distance and name of the object into the console
                 Debug.Log(hit.collider.name);
                 Debug.Log(hit.distance);
                 SnapToWalls();
             }
             else
             {
                 //the ray isn't colliding with anything
                 Debug.Log("none");
             }
         }
         
         void SnapToWalls()
         {
             //variable for the distance of the ray (never greater than 1)
             var rayDist = hit.distance;
             Debug.Log(rayDist);
             //If the players raycasting hit a wall (always less than one if so)
             if(rayDist > 0)
             {
                 if(rayDist < 1)
                 {
                     //Only if player left the ground (jumped)
                     if(!TP_Controller.CharacterController.isGrounded)
                     {
                         //change gravity
                         TP_Motor.Gravity = 11f;
                         //then have the player forced forward somewhat (even if they dont push forward - more so if they do)
                         TP_Controller.CharacterController.Move(transform.TransformDirection(Vector3.forward) * Time.deltaTime * 2);
                         //and output blah into the console
                         Debug.Log("BLAH");
     //HERE IS WHERE I NEED CODING TO MAKE MY PLAYER WALL WALK :(
                     }
                 }
             }
             else
             {
                 //go back to normal
                 TP_Motor.Gravity = 21f;
             }
         }
 
 }

what this does right now is move the player forwards a little, and if they are pressing forward it moves them faster, later ill animate the character like he is running along the wall.

but i need to make it like he is only moveable in two axis's of the world, or maybe only one, if he is going straight up a wall with a ray thats going forward detecting a wall.

for now I cant think of a way to do it, I tried clamping but couldnt quite figure it out, how to get the raw like world coordinates of my player then to force any (X or Z) to be stuck at a number I set. that way he moves sort of along the surface of a wall.

anyone know how the make my player move along a wall, still being effected by gravity from my motor? what are other ways to make that effect?