The way vibrato is used in gypsy jazz violin, like Stephane Grappelli is a bit different from normal classical playing. Typically only used on long notes and developing after the note has sounded, possibly a bit wider too. Is there a way of notating this, and would it be difficult for a player who is not used to it? This is for a string quartet with a bit of gypsy/balkan influence
Just to clarify, you're describing an out-of-the ordinary vibrato used as an ornament only on certain notes, not simply an unusually wide variety of the "switch it on, leave it on" vibrato common to modern practice. I've seen Mark O'Connor elaborate on this idea of a extremely wide vibrato ornament, a sort of "vibrato trill," in which he actually shifts his hand rapidly up and down roughly one position, allowing his finger to actually slide up and down the string in an oscillating glissando (unlike normal vibrato, in which the finger stays anchored in place and merely "rocks" back and forth). Considering that Mark O'Connor studied with Stephane Grappelli, he might well have inherited the technique. (This isn't the best example, but you get the idea:
Short answer: No, there isn't a standardized notation for such an ornament. I'd suggest inventing one and explaining in a text note at the outset. Maybe the horizontal wavy line used to extend trills, with something like
vib. at the beginning of it? Or
w.v. for "wide vibrato?"