No, you can't. You can only activate the "when an effect trashes this card from the security stack" when this card is directly trashed from the security stack.

It refers to when the total number of cards in both you and your opponent's security stacks is X or fewer. The text "if there're 6 or fewer total cards in both players' security stacks" would include when there're 3 cards in both players' security stacks, 2 cards in your security stack and 4 cards in your opponent's security stack, etc.