Pass "external" uv's to shader

Hi, I'm trying to draw to a texture dynamically mimicking paint on surfaces.

My current setup is as follows. I render a stamp texture with Graphics.DrawTexture to a render texture that is later used by my shader to display the paint.

         float xPos = UV.x * rt.width;
         float yPos = UV.y * rt.height;
 
         RenderTexture.active = rt;    //Set my RenderTexture active so DrawTexture will draw to it.
         GL.PushMatrix();                      //Saves both projection and modelview matrices to the matrix stack.
         GL.LoadPixelMatrix(0, 512, 512, 0);    //Setup a matrix for pixel-correct rendering.
 
         //Draw my stampTexture on my RenderTexture positioned by posX and posY.
         Graphics.DrawTexture(new Rect(xPos - stampTex.width / 2, (rt.height - yPos) - stampTex.height / 2, stampTex.width, stampTex.height), stampTex, mat);
         GL.PopMatrix();                                  //Restores both projection and modelview matrices off the top of the matrix stack.
         RenderTexture.active = null;            //De-activate my RenderTexture.

For simple meshes this work's fine as shown here:

When it comes to more complex meshes, like my simple character, the paint isn't applied consistently.

So i created a material that i pass on to Graphics.DrawTexture to handle the mapping. The problem is I have no idea how to accomplish something like that. How do i map my splat texture to the render texture with my character's UV-set? So that the texture is rendered correctly. Thanks!