For what your trying to achieve (I think) it should be:
Computer -- S
AE -------- W
Computer -- I -------- Speakers
Computer -- T
Computer -- C
Computer -- H
Replacing the switch with your splitter (but using it effectively the wrong way round) may work for you.
This is all based on the understanding that the AE is one source of audio for your speakers and your PC is another source of Audio for the speakers, if this isn't the case then you need to explain what you are trying to achieve.