"In general, in case of import of personal and household effects by a person normally not residing in the Community does not require an export or import permit when the person is taking up residence in the Community, except in the case of Annex A species."

https://cites.org/sites/default/files/eng/resources/ref/E041-EU.pdf

My emphasis. It is not clear what the position is for a visitor. There are exemptions and exclusions, but finding out what they are in clear and understandable form, and which you could show to a customs offical is difficult.

More info here, but no definitive answers:

https://www.ismtrust.org/advice/cites-and-the-rules-for-musicians

Of course CITES only applies if your instrument contains materials from a protected species. The value of the instrument will also be a factor - if it was fairly cheap and easily replaceable you might be willing to take a change, if it's worth thousands you will be more cautious.

This article suggests things should be come easier, but again finding the specific regulation is difficult:

https://reverb.com/news/cites-restrictions-on-musical-instruments-could-be-coming-to-an-end