I believe in the options that you can set different sound devices for ring and voice. I'll check when I get home from work to be sure.
EDIT:
Under audio settings in the ring drop down, there is a "ring on all devices" setting. You should be able to set that. Of course, if your speakers mute when you've got the headset problem, this isn't going to fix it. That's not a Skype problem though.
If you have reassiable jacks (most everything does these days), the just set both the jack that your speakers are plugged into and the jack that your headset audio is plugged into to Line out. That way they will both play all of the time.