We're doing a medical thriller on a very small stage.  One of the climactic moments involves a character being given an injection downstage center, about three feet from the audience.  The audience has to see the syringe, and the needle, and ideally even the spurt of liquid out the tip of the needle... but we obviously don't want the actors struggling over a sharp and potentially dangerous needle, either.

Anybody know where we can get a realistic fake needle, preferably circa 1968?  Or does anybody have any other suggestions?

Further to Larry?s excellent  suggestion. You could use a piece of fine fibre optics! It will give a better appearance of a  metallic needle, more so than  electrical spaghetti. Being a tube it will also pass any liquid, which can be mopped & masked, with cotton wool or swabbed up in full view of the punters