Hello, I am following up on a twitter request by one of your users. We recently launched the Skype Share button. The configuration page is available here: https://www.skype.com/en/create-share-buttons/

We offer a JS button with SDK. We also offer a raw URL option. The URL is:
https://web.skype.com/share?url=<urlencoded_url_to_share>&lang=en-US&flow_id=&source=JetPack

Expected usage, with ideal window size:
function shareUsingSkypeRawLink() {
window.open('https://web.skype.com/share?url=<urlencoded_url_to_share>&lang=en-US&flow_id=&source=JetPack’, ‘_blank', 'toolbar=no, scrollbars=yes, resizable=yes, width=305, height=665');
return false;
}
<a href=‘javascript:void(0)' onclick="shareUsingSkypeRawLink()"> Share using link

Asset available here:
Skype logo file is available here: https://swx.cdn.skype.com/skypewebsdk/shareButton/v/latest/assets/images/s_logo.svg

We also have a WP plugin: https://wordpress.org/plugins/skype-share-button/

Please let me know if you need any other information.
Thanks,
Amit Paunikar
Product@Skype