If you have inflict less damage in co-op, it depends how many people are in the game that determines how many knives it takes to kill a scout. For example, if there are only 2 of you in a co-op game and you use that relic, that person will need to only knife 2 times for a kill. If there are 3 or 4 in the game, the person using that relic will need to knife 3 times for a scout kill. This is purely based on the fact that more players = more health enemies have.
I'm confident that NO relic affects everyone. I am confident in saying that ALL relics are individual based. If I am somehow proven wrong, or at least there is some proof/evidence to support the fact I am incorrect (which makes no sense to me if so), then I will happily accept that, or if the devs can actually chime in and let us know whether or not relics are for the INDIVIDUAL or for the TEAM. It just makes no sense at all that any relics will affect the entire team.