Pernambuco (Caesalpinia echinata) and ebony from Madagascar contained in finished musical instruments or bows are exempt from certificate requirements.
Only the first export from Brazil of Pernambuco bows requires a CITES permit. However, if you travel to Brazil with a Pernambuco bow, it is recommended to have an expert certificate attesting to its origin in order to avoid any confusion during possible controls at the exit of the country.
If your instrument is exclusively made of species that are either exempt from certificate requirements or not protected by CITES, you can travel safely without this document. Be cautious though, as the presence of one single protected species may require a certificate (MIC or TEC). If your instrument contains a species exempt from certificate requirements, always check whether it also contains species requiring a certificate.