Answering the question's update to consider ULEZ.

According TFL's text description of the boundary of ULEZ:

Heathrow Airport is inside the ULEZ, as are the roads bordering it and the entrances into it.

You can also see on the map that it extends East, North and a fair bit South too.

So your best bet would be to get a bus to the West. The nearest stop I can obviously spot is Moor Bridge (Stop L)

https://tfl.gov.uk/modes/driving/ultra-low-emission-zone/ulez-boundary-description

site ULEZ covers all of the Heathrow airport

Answering the question's update to consider ULEZ.

According TFL's text description of the boundary of ULEZ:

Heathrow Airport is inside the ULEZ, as are the roads bordering it and the entrances into it.

You can also see on the map that it extends East, North and a fair bit South too.

So your best bet would be to get a bus to the West. The nearest stop I can obviously spot that is outside the ULEZ and is accessible by a single bus from the Heathrow Central Bus Station is Lakeside Road which the A4 and 7 stop at, on their way to Slough. The buses seem to run every 30 mins and the journey is 11 minutes.

Looking at the stop on Google Street View it looks like there's a bit of laybe there as well, so it looks like a car would be ok to stop there

I assume you've actually checked the vehicle is non-compliant on the TFL site as I've seen some misleading articles about which vehicles would have to pay.

Also some different buses seem to call at Terminal 5, so if you're landing there a different bus route may apply.