Without a doubt, the letter was the one Lin Yi wrote at the Nakajima auction. He didn't lack spirit jades anyway, and he just wanted to give it a try. Even if it didn't reach everyone, Lin Yi wouldn't feel that regretful. However, he probably didn't even think that the letter would actually reach them.
For safety reasons, the letter didn't go into any secret information. Lin Yi basically told him everything that happened after he came to Tianjie Island, from the Ying Xin Pavilion to the central island, including his meeting with Tian Gang and Xue Li.
He didn't mind the hassle because he wanted everyone to know that he was safe and that everything was going well on Sky Class Island. He also wanted everyone to have a general impression of Sky Class Island.