My father had to lay off a bunch of people in 2008. I am now a manager. He told me that if I am ever forced to do this to not ever do this crap to my team. Tell them that this is bullshit. Tell them that you are upset. Tell them that you haven't slept. Tell them that the are right to be mad, disappointed, and even to hate you for choosing their head to roll. Anything better than fake smiles and "I'm sure you'll land on your feet."
For me, I think I'd just quit if I was told to lay off people on my team. Maybe that's hard to do in the moment, since I'd also not want to lose my job in a major crisis, but it sounds awful.