The term "Jews Harp" is of great age, and is not pejorative by any means.

Not pejorative? Given the historic context for an instrument whose humble, lowly, inexpensive and ultimately portable ubiquity is its defining feature I'd say pejorative is exactly what it is. Calling such a thing a 'harp' is pure mockery; in the context of anti-Semitic racial stereotyping it is doubly offensive. Similarly 'Witches Trump' carries echoes of persecution and misogyny despite many folklorist attempting to hike the term to the magical qualities of iron (were they played by witches? or carried as a charm against them?)   

The matter needs much sensitivity, and whilst happy with the term Jew's Harp historically I accept the problems which inclines me to favour J-Harp in modern use as the general heading for what is a vast and fascinating topic. I've lately heard Jarp, but I'm not convinced! Just because something is 'historic' and 'traditional' doesn't make it acceptable. As has been pointed out, there are countless types of J-harp, each with their own own colourful name - Jack. C mentions Scacciapensieri, always a favourite with the kids I work with as literally it means 'Thought Scatterer'!

One would hope any J-harping storyteller coming into contact with kids is so equipped as to be able set such issues into context without having to fear the 'Political Correctness Gone Mad' brigade for whom 'folk' will always be a means to culturally autistic outrage. Give me Political Correctness over Folk Correctness any day!