The original Seahaven Towers by Art Cabral I played circa 1989 on a Mac II had very subtle sounds when you moved cards. I think it could be a great addition to Seahaven Towers here. It might be enough to simply crib the sounds from the original. You can watch a video here:
You can try it by downloading the ".hqx" file from https://www.macintoshrepository.org/4230-seahaven-towers and dropping it on the Mac window screen, then digging around in the "Downloads" folder inside "The Outside Word", and then dropping it on "StuffIt Expander" (the unzip-like utility of the era). You'll be left with a double-clickable Seahaven Towers app. It doesn't look like much now, but at the time it was revolutionary.
The sounds are stored as "snd" resources in the resource fork. I've extracted them and converted them to .wav and put them in a zip file here, so give it a go.