“No war but class war” will instantly be recognized as a leftwing phrase. At best, a few people will nod along. At worst, someone in management will realize what it is and use it to discredit you. “See? Unions are bad! They’re full of communists who want to steal all your food by collecting dues! They’re no better worse than nazis!” is what they’ll say and people will gobble it up.

The phrase I’d use instead is “Owners/management/executives aren’t your friend.” You need to call out the bourgeois for what they are without using leftist terms. You can spread class consciousness by showing your coworkers how the people above call them family, but don’t treat them like that. You can point out how the CEO doesn’t know anybody’s names and never invites them to personal events, something actual family does.