About every imaginable combination of Minhagim exists for what to do with music during the 3 weeks and S’fira. We don’t pick and choose Minhagim. Ask your father or your Rav what your Minhag is and be happy following that.
(Of course if your Minhag permits listening to any a capella but you don’t want to there is no obligation to. However, if your Minhag is to Asser any recorded music, even slow and heartfelt, then you cannot listen to that type of music just because it feels appropriate for this time. There are other branches of Judaism that do things based on what “feels” proper. Orthodoxy isn’t one of them. My advice would be to skim through all of your a capella music and make yourself a playlist/CD of slow a capella songs that you think will inspire you during this time.)