I suppose Lethal injection is the safest way to ensure you're gonna die painlessly, though all the waiting and strapping down would probably freak me out way more than standing in a courtyard several meters away from a squad of riflemen. But since i doubt firing squads aim for headshots, it wouldn't be painless, then no way would i pick that or any of the other methods were a quick and painless death is not guaranteed.
Of course, the best case scenario for a non-natural death is freezing to death. Eventually u just get tired n sleepy, n then u just fall asleep in the snow, never to wake up...
Dunno if that counts as an "execution" tho.
On a side note, capital punishment is sick and wrong, whatever form it takes.