Although you could call a paint event manually, by constructing a PaintEvenArgs instance for yourself, and calling the method, it's a poor idea.
PaintEventArgs pea = new PaintEventArgs(MyGraphics, MyClipRect);
pictureBox1_Paint(pictureBox1, pea);
A better solution would be to move the code out of the Event handler into a method, which you pass the Graphics Context from the Paint event, and then call that instead, supplying a Graphics object suitable for the painting (and remembering to Dispose it when the method returns)
However, if your skinning mechanism is not passing the Paint events on down you your controls, then you need to look at it and find out why - as it would disable all "clever" graphics effects and probably make many, many controls fail. Are you sure you are calling Invalidate on the correct controls to initiate the Paint in the first place?