I do believe a tape is a kli shir.
There is a gezeira all year round against listening to music or singing. What the parameters of that gezeira are, is debatable, but klal yisroel seems to have picked the minimalist approach, even though it is not consistent with the way we would normally pasken.
Rabbiofberlin correctly points out that there is no basis for a new ban on music. Because it is already assur, and whatever applies the whole year, applies during sefira too. New issurim, we don’t make. So wherever and whenever music is mutar during the year, it is mutar during sefira too.
While others may not agree with this view, it is what my rav holds and how I am noheg.