No letter is generated for short-term letting. Condition 19 prohibits it outright, so sending a notice would not make it lawful — it would only put the intention in writing to your council. Choose a different use, or apply for full planning permission.
The exemption only answers whether you may build. A room-by-room heat loss calculation, a sizing cross-check and a red-flag list on your quote give you the auditable basis you were never handed.