This leaves the regular heating oil system completely intact.

For your waste oil you need to make a small non-aerated vaporizing chamber which is nothing but a coil of steel tubing sitting in the flame cone of the kerosene flame.

The end of the tubing is a small jet head.

The filtered waste-oil is slowly pumped down through the spiral (in the flame) and it vaporizes inside the tubing. There's no air in there so there's no way for it to ignite.  It just boils.

The jet hole is at the bottom of the spiral, pointing back across the spiral.

You need a check-valve, a flow control, a pressure regulator and a slow-flow pump for the waste oil.

The jet tip should be a very small opening since you don't want it to easily flow liquid oil. But it should easily pass the vapor.

When the oil vaporizes inside the tube, the vapor passes throught the tip easily and then ignites when it hits the open air and flame. Some of that waste-oil flame heat is used to keep the vaporization process going.

You can use the same basic photocell circuit to monitor the flame activity.

The kerosene flame starts, the waste-oil system is heat-primed and ignited, and then the kerosene system shuts off again, leaving the waste-oil to do it's thing.

OR

Just put a severely under-capacity jet tip on the kerosene gun and run both at the same time, all on the same circuit. No mixing of the oil with any other fuels is really necessary.

BUT, you can add other types of oil as you want because it will all be vapor before it hits the flame front.