How not to get a null pointer when copying an instance without using shared_ptr

There is a code structure I use a lot and I always face the same problem. I have a class which contains several pointers, and every time I copy it, I can't read into my pointers anymore because I'm not using a shared_pointer and my pointers have been deleted.

class Mesh
{

public:
    ~Mesh()
    {
         // Delete all pointers in vertices
         ...
    }

    Mesh processOnMesh();

    std::vector<Vertex*> vertices;
};

Is there a trick commonly used for this which does not involve using a shared_pointer ? I am asking this because I use a large amount of pointers (10 000 to 100 000) and I don't want to create a new instance for each pointer.