Help Finding Specific HDMI Adapter

[Chiakuu]

Hello, I finally got myself a television! The television that I got has great built in speakers, and I wish to use my Wii over HDMI - I have an adapter arriving soon, but it splits the Wii video/audio connector into an HDMI connector AND a separate audio jack. I know it must exist, but I am looking for an adapter that will take that HDMI port and audio jack and combine them together into an HDMI cable that carries both video and audio. What keywords and what adapter am I specifically looking for? The only results I can find are the opposite - taking an HDMI/audio cable to the separate HDMI and audio jack. Unfortunately, it looks like this television does not have a separate audio input for the HDMI connectors, and the speakers are way too good to justify buying a cheap (and most certainly worse sounding) soundbar.

Thanks!