At first, I would like to share my experience to try to avoid waste of time and frustration to some of you.
I have been using Skype 184.108.40.206 on Linux Mint 18.3 Cinnamon, kernel 4.10.0-42 without any trouble.
After upgrading to 220.127.116.11, my webcam (logitech C525) is not found anymore by Skype ("no device found" error).
Getting back to 18.104.22.168 on exactly the same system allows me to recover all functionalities.
Actually, I made a mistake I corrected after my initial posting, upgrading to 22.214.171.124 works fine as well. It is the 126.96.36.199 that Mint offers as Preview which is an issue.
Then, @Microsoft support : at your disposal for any additional information if you would like some tests to be performed.