Is there a slip cork that will actually work when using a 1/64-1/32 oz jig and 4-6 lb line without adding additional shot weight?
Slip bobbers that will balance with the weight and line size you mention are available.
That said, I have not had much success with that combination. The jig will take forever to pull the float upright. Four pound line is too heavy for the light jig. A few years back there were numerous articles in fishing magazines touting very light bobbers, little or no weight and line sizes as small as 1/2 lb. I spent a fortune buying European style floats to try the technique.
My greatest success has been with a 7/8 inch diameter balsa slip float balanced with a #3 split shot. A #3 split shot weighs 4.31 grams, or roughly 1/6 oz. I suggest you try a 1/2 inch balsa float with the 1/64 ounce jig and a small split shot about a foot above the jig, just heavy enough to hold the float upright. Any smaller float has no advantage that I have found.
The Waco Kid uses 1/64 ounce jig heads for big bream. You might ask him how he rigs it.