If possible you could also place a tee before the skimmer pump input, this way you could feed the overflow water directly into the skimmer pump rather than the skimmer body. If you did this you wouldn't have to worry about eliminating the overflow bubbles from the skimmer feed. It may even be beneficial to do the exact opposite as the previously posted schematics and send the highly aerated water to the skimmer while the lower aerated (quieter) water is sent into the sump.
I've has these pictures lying around from a previous project. Obviously not the same as your setup but I think the idea is the same.
HTH