The ukulele also called Uke, is a member of the lute family of instruments of Portuguese origin and popularized in Hawaii.
(Wikipedia)
Cithara Havaiana is used in Vicipaedia but it seems wrong since this instrument is of Portuguese origin and that it is closer to a testudo rather than a cithara (I think?).
What would you use?
Edit Cithara Lusitanica refers to another instrument.
The Wikipedia article on ukulele mentions that it was "developed in the 1880s, the ukulele is based on several small, guitar-like instruments of Portuguese origin". The instrument was not in existence before that, and there was no word for it. If you want to stick with Classical Latin, the question has to be shifted from "What is ukulele in Classical Latin?" to "What would the Romans have called an ukulele?", and this new question is necessarily speculative.
There does not seem to be a well established Latin name for the ukulele in Latin of any era. If you want a translation, it is important to know the purpose:
If the purpose is to call it what the Romans might have called it, then a cithara or testudo of some sort sounds likely. (Wikipedia mentions that the ukulele is in the lute class, so testudo might be closer. Both make sense. Wikipedia lists some Roman string instruments.) If we are to associate it with Portugal — which, unlike Hawaii, has the benefit of being known to the Romans — then cithara/testudo Lusitanica sounds right. The Portuguese guitar whose Vicipaedia article you link to did not exist at the Roman time either, and it could well have earned the same name in Roman speech.
(It is likely that the Romans would have named the instrument after where they found it, not after where it was originally from. Thorough research and thought before naming is rare, and we should not expect it. This is indeed why the ukulele is considered Hawaiian: it is commonly found there. The translation chosen by Vicipaedia makes sense.)
If the purpose is to write about the instrument to a modern audience, then you had better call it ukulele in Latin. Or perhaps modify it to uculele or even uculela. If you choose anything else, chances are that the word will fail to communicate what the instrument actually is. Language is mostly used for the purpose of communication, and that brings many practical constraints. Many people know the word "ukulele" but few know enough of its origins to connect it to any other name you might come up with, no matter how logical.
If you go this route, you have to choose how to decline the word. If the word only appears a few times, then the undeclined ukulele is a good option, perhaps paired with a word like cithara/testudo or instrumentum to give a hint of its nature and carry visible case markings. If you use it more often, it is convenient to make the word itself follow a declension. The most obvious options seem to be (with C or K as you prefer):
If the purpose is something else, then the translation might be something else.
Unfortunately there is no unique and correct answer. What you should do depends on what you want to achieve, but my general suggestion would be simply ukulele or perhaps uculela. This is the case with translations more often than not, especially with things that have a well known name across various languages. (Cf. opossum.)
