One week after wrapping the exhaust I finally had the opportunity to finish the job and spray the header with the silicone sealant. I used some painters' tape and paper to cover surrounding parts and applied several coats wherever I could get with the spray can. There might be a few areas on the inside that aren't covered 100 per cent, but most of the wrap has been treated.
Added bonus: The stains on the exhaust header flange and the screws are now painted over black and look much more presentable!
I left the car with the hood up for a couple hours to dry, and when I drive tomorrow the sealant will properly cure when the exhaust gets hot.
I hope the sealant won't stink too bad as it cures, because the wrap developed a pretty penetrant smell that has finally gone away after a week of driving. I was lucky that the first few days it was curing the weather allowed me to drive with the top down!