I don't think Skype for web SDK team has any intention to provide Recording or Cognitive analytics ability to Web SDK in the near future. So i decided to go with alternative ways.
After a lot of research, i have decided to use Skype Media bot along with Skype Web SDK to record audio and video conversations.
- Create a Skype Media Bot and add Skype for Business as channel.
 
- Register this bot with Skype for Business online ( Only Tenant Administrator can do that)
 
- Make sure in each conference, this Skype Bot is also invited by default. So this bot is a participant in each conference call. It records audio and video.
 
- Skype Bot has simple interface to Record, Respond, Convert audio to text and many more features.
 
Github samples can be found here
Skype Bot framework has NodeJS and C# APIs.