The real question is what is the Issur? The answer is nothing. We are supposed to avoid Simcha during Sefira and the 3 weeks. Music is not one of the things mentioned in the Shulchan Aruch. Dancing is mentioned in the Magen Avraham. So everything to do with music, or recorded music, or just a capella, is dependent on Minhagim. There are many different Minhagim. Most Chassidim actually have the Minhag that makes the most sense. They will listen to slow songs but not fast songs (since we assume that the issue with music comes from the Issur of dancing), regardless of a capella or instrumental.
There is little reason in the Halachic literature (aside from a Teshuvah in the Shevet Halevi, who has a great Svara but it’s not mentioned in the earlier Poskim on this issue) to differentiate between listening to a capella music and singing to oneself. That’s just something to keep in mind.
Lema’aseh, it’s very hard for anyone to give an actual P’sak on this. The best Eitzah that could be given is that if it causes you actual Simcha then you should probably have the Seichel to avoid it. (Simcha is very different than happiness. I once had someone complain to me that they find it very hard to be inspired during the 3 weeks because they can’t listen to inspiring music because that makes them happy. The goal is not to avoid any happiness or inspiration. The word “Simcha” should more accurately be translated as “joy”. We are supposed to avoid things that make us exceedingly happy or joyful.)