Both switches depicted in the diagram are controlled by the same breaker. The other two switches in the box which aren't labeled are controlled by two other breakers. Since I only want to replace one of the switches with a Wemo light switch, can the Wemo share the neutral wire as the second switch that I am leaving in place? Currently the neutral wires are going straight up to the lights bypassing the switch, so I wasn't sure.
Yes, you can connect to the same neutral that's currently part of the switch circuit (the source neutral, really). Be sure to leave all existing neutral connections intact.