Welcome to the forum!😃
To answer your question: If your thin client has an audio in port it can likely be configured to mix the line in signal into the output. Look for an option like that. Ortherwise I'd suggest getting an inexpensive external mixer so you don't have to switch the cable between inputs all the time. Makes your life a lot easier.😉
By the way: This part of Vogons ('The Guide') is dedicated to getting old games to run on newer systems and supported OS.
The thin client topics are about older hardware and unsupported OS, so they're supposed to go into the 'Marvin' subforum. Your previous thread had been moved accordingly.
This topic is probably best suited for Marvin->Sound. You will get better support there and the forum is kept orderly.
I'll ask the mods to move the thread for you.👍