There are multiple layers to this. Using voices to create the instrumentals in a song vs just doing true vocals and harmonies. Fast and/or upbeat music vs slow and/or solemn music. Parodying non-Jewish songs vs recreating Jewish songs, vs original music (the category most likely to be deemed 'appropriate' for sefira/3 weeks). It may not be the most common form, but there are definitely albums with vocal/harmony singing only, no upbeat/fast stuff, and Jewish only. During the 3 weeks I always listen to Im Eshkachech (Suki and Ding). Recently I was listening to Around the Campfire from MBC. I see Kumzitz in the Rain is up to 5 albums now. And I'm sure there are plenty of other good ones.
According to all the
Poiskim I saw, Once you have singing coming out of a "device" it's considered a
kli shir, it dons't matter if there is is just one man singing.
The mistake people make is thinking that only musical instruments are not allowed, however (again according to the
Poiskim I saw, very possible there are others who disagree) anything considered a
kli shir is not permissible, and that includes device playing acappella.