Presumably the ships are compartmentalized. You only need vacuums powerful enough to vacate a single compartment, then you just need as many vacuums as compartments.

This supposes that the signal must be “sent.”

Orson Scott Card in Ender’s Game came up with an Ansible which worked via two entangled particles - you could spin one and the other would spin the same no matter how far away it was.

This probably isn’t actually possible, but I think in our hypotheticals it’s fair to consider a form of communication in which the information doesn’t travel faster than light, because it doesn’t travel at all, it simply exists at both ends.