A much-awaited feature may be coming soon with one of the near-future Redstone 2 Builds. Leaked video posted by Windows Blog Italia shows that Skype + SMS integration is present in one of the internal Windows 10 Mobile builds under testing.
Check the video below that shows how one can use the Skype app for both SMS and Skype chat. The Messaging settings will also allow one to select the default messaging app and you need to select Skype as default, if you want to use it for SMS too.
Thanks Anto for the tip. Cheers!!