John Stowers (the GNOME Tweak Tool developer) has updated the old skype-notify Python script to work with the new GNOME 3 notifications.
The updated Skype-Notify script respects the new GNOME3 notification capabilities like showing transient or permanent notifications, etc., however, you can't reply from the notifications.
Get GNOME3 Notifications for Skype
1. Download the python script from HERE, extract it and place the script somewhere - let's say in a folder called "skype" in your home directory.
2. Make the script executable. If you've placed it in the "skype" folder in your home directory, run this command:
chmod +x ~/skype/skype-notify.py
3. In the Skype options, on the Notifications tab click "Advanced View", then check the "Execute the following script on any event" box and under it, paste this:
/path/to/skype-notify.py -e"%type" -n"%sname" -f"%fname" -p"%fpath" -m"%smessage" -s%fsize -u%sskype
In the above command, replace "/path/to/skype-notify.py" with the path to where you've placed the skype-notify.py script (like /home/YOUR_USERNAME/skype/...).
And you are done. Now the next time you'll receive a Skype notification, Skype will prompt you to authorize the script - check the "Remember this selection" box, then "Yes" and you are done.
At this point, you'll receive both GNOME3 and Skype notifications in the same time so if you want, you can disable the original Skype notifications (from the Skype options, on the Notifications tab, click "Advanced view" and then select each notification and disable "Display popup notification").
Thanks to John Stowers for the tip!