Here’s my take on this.
Your best first step might be the simplest. Skype’s call history is typically stored on their servers, not just locally on your iPhone. Try logging into your Skype account on a different device, like a desktop computer or through a web browser. There’s a good chance the call log you cleared from your phone is still perfectly intact and accessible there, as the deletion may not have synced everywhere yet.
If that doesn’t work, restoring from a previous iCloud or computer backup is another option. The main pro is that it’s very likely to recover the log if the backup was made before the deletion. The significant con, however, is that it will revert your entire phone to that point in time, wiping any newer data. I’d definitely check your account on the web first.