Finding an appropriate alternative to textures

Hello everyone,

first of all, I want you to know what I'm trying to do and what I got so far:

In Unity, I set up an object on which I am trying to display websites, being able to interact with them. The surface of the object is not flat, it looks more like a curved wall:

In addition to the website itself, I want to display a simple mouse cursor (by now a simple black rectangle, maybe a crosshair in the future), indicating the current mouse position. The way I'm achieving this right now is to use a mesh renderer component attached to the gameObject, containing two materials and two scripts, manipulating the material's textures. To get an overview of the scripts and materials I attached to the gameObject in question, see the following screen capture of the inspector panel:

The first material uses a diffuse shader and its texture is manipulated (overwritten) by the script providing the webView ("WebTexture"). I believe this likely to be non-optional since I'm using a Unity plugin called "uWebKit" to provide this kind of functionality.

The second material instead uses a transparent/diffuse shader and its texture is overwritten by a script i wrote on my own ("mousePointerTexture"). My script creates a texture having the same dimensions than the texture of the website. Almost every pixel of my texture is transparent except for a few pixels which are black, representing the mouse cursor. To get an idea how I do this, please see the following script:

 using UnityEngine;
 using System.Collections;
 
 public class mousePointerTexture : MonoBehaviour {
 
     // dimensions of texture
     int dimX = 1920;
     int dimY = 1200;
 
     // background color, transparent
     Color bgColor = Color.clear;
     // color representing the mouse cursor
     Color crsrColor = Color.black;
 
     // resolution of application window
     int resX = 1280;
     int resY = 800;
 
     // texture on which the mouse cursor appears
     Texture2D texture;
     // scaling factors for the mouse position
     float scaleX, scaleY;
     // mouse position relative to the app window
     Vector3 mp;
     // calculated mouse position on the texture/website
     int mx;
     int my;
 
     // list of materials the renderer contains
     public Material[] materials;
 
     // colors being used by setpixels()
     Color[] colorsCRSR;
     Color[] colorsBG;
 
     // Use this for initialization
     void Start () {
         // calculating scaling factors
         scaleX = (float)dimX / (float)resX;
         scaleY = (float)dimY / (float)resY;
 
         // initializing texture for mouse cursor
         texture = new Texture2D (dimX, dimY, TextureFormat.ARGB32, false);
         for (int i = 0; i < dimX; i++) {
             for (int j = 0; j < dimY; j++) {
                 texture.SetPixel(i, j, bgColor);
             }
         }
         texture.Apply ();
 
         // get renderer's materials
         materials = renderer.materials;
 
         // setting texture as 2nd material's mainTexture
         (renderer.materials.GetValue (1) as Material).mainTexture = texture;
 
         // initializing colors
         colorsCRSR = new Color[4 * 8];
         for(int i = 0; i < (4*8); i++) {
             colorsCRSR[i] = crsrColor;
         }
         colorsBG = new Color[4 * 8];
         for(int i = 0; i < (4*8); i++) {
             colorsBG[i] = bgColor;
         }
     }
     
     // Update is called once per frame
     void Update () {
         if (materials.Length == 0) {
             return;
         }
 
         // get new mouse position
         mp = Input.mousePosition;
         // calculate corresponding position on webSite
         mx = (int)(mp.x * scaleX);
         my = (int)(mp.y * scaleY);
 
         // set pixels representing the mouse cursor black
         texture.SetPixels(mx, my, 4, 8, colorsCRSR);
         // push to GFX card
         texture.Apply ();
         // set pixels transparent again
         texture.SetPixels(mx, my, 4, 8, colorsBG);
     }
 }

As you can see, I use the known to be slow texture.SetPixels()/texture.Apply() combination. And this is exactly where my problem is: As you probably could imagine, the single line of

 texture.Apply ();

causes the framerate to decrease from 60fps by 20 to 40fps. I'm aware of my method not being adequate in this case, but other solutions i read about, like using faces of triangles, looking not that simple in my case, considering the object I'm working on being non-planar.

So here is my question: Is there an appropriate alternative to textures to fulfill my needs?

Any answers, suggestions and even the tiniest hints will be much appreciated.

Thanks for your patience.