i've also had the same issues with skype not working since i upgraded to WM6.1. Did some research a few weeks ago, and even though its not exactly skype, im using a program called Nimbuzz which works as skype. Same log in info and all that. I've been able to chat with it and indeed make calls. Still the same deal though were you have to use your headset or else the sound will only play out of the speaker.
http://www.nimbuzz.com/