All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
All that is slaughtered by the people of the Book (Christians and Jews) in their customary way of slaughtering is lawful to us. We can eat it, sell it and buy it. Allaah Says (what means): {Made lawful to you this day are all kinds of lawful foods. The food of the people of the Book is lawful to you and yours is lawful to them.}[Quran 5:5]
However, every animal that they kill by other means than cutting the throat like by electrical shock or clubbing to death is considered as Maytah (any meat whose animal was not slaughtered in the usual way). It is also forbidden to get any profit from it.
As for the electrical shock you mentioned, if it is very light and is not used to kill the animal but rather to prevent it from moving while it is being slaughtered, it is lawful and its meat can be eaten by Muslims. But it is better not to eat such meat as harming an animal in this method is not lawful. The method of scrutiny you follow to find the truth about the chicken you import is enough and you should accept what those responsible of the slaughter house tell you as long as you have not found something doubtful from their side that make you suspect them.
Allaah Knows best.