State your emergency fuel early

You can but there really is no sense in declaring an emergency with 2 minutes of fuel remaining. You need to stay on top of your fuel situation and report earlier with say 30 or 20 minutes of fuel remaining.

The response on the controller’s side is, please divert to the nearest airport, frequency change approved.

We, ATC, try to accommodate to the best of our ability fuel emergencies but you always need to remain aware of your situation. How much fuel is remaining and do you have a backup plan to land safely. You are not bothering us by giving us advanced warning.

We will and have landed aircraft on inactive runways, just check out Wideroe 1 at 6:52 of this time-lapse. It is highly satisfying when that works out, by the way. In that case all departures were stopped to allow for the aircraft to safely land.