In the Links tab, add a Skype icon and add the following text, replacing "yourskypename" with your actual skype name, next to the Skype social icon in the opened link field:
For example, skype:emailsigrescue?call OR skype:emailsigrescue?chat OR skype:emailsigrescue?add
You can add the "call" function which will initiate a Skype call when clicked, a "chat" function which will start a chat, or the "add" function which will add you to their skype contacts list.
TIP: It's a good idea to turn on short URLs if using Skype links so they work in all email clients (like Gmail). Go to Profile > Settings and turn on Short URLs. You can turn on short links either Per Link or All Links. If you turn it on Per Link, make sure that the Short URL box is ticked on the Skype link box.