I would get some branches not sprayed with pesticides just to be safe. It seems dormant oil can be toxic towards your plants and insects that aren't pests or disease causing, as neem oil seems to kill insects at various stages after being applied to plants and surfaces. This is only what I've been able to find on this.
However, we do use the method of washing plants and other vines just in case they've been exposed to pesticides with a warm soap and water mix with thorough rinses. My only concern is how deep might the oil have already saturated the branches you have even though its dry, and if higher temps might force some of the oil to the surface of the branches where your chameleon might have a chance to ingest some of it (drinking water off them).