Hello Starrykitten,
I hesitate to offer advice, as I've only been playing the theremin just a few weeks short of one year, (although I'd like to think that by now I've settled into a style of playing that suits me best, even if I still have much to learn). Anyway, rather than advise, I'll share a few of my observations; make of them what you will.
The width of vibrato is, to an extent, a matter of taste. Don't expect your playing to ever please all listeners; try to find what sounds right to you. But that needn't, in my opinion, be just one vibrato sound.
Personally, my handling of vibrato tends to vary according to either the theremin I'm playing or the piece of music. With one theremin I favour a flute-like whistling "voice", (for which I use the least vibrato) and sometimes a voice that reminds me of a human soprano, (which seems to work better with a little more vibrato). My other theremin suits a mellow brass-like tone that suits a slower narrower vibrato, and a very cello-like voice that works best for me with a wider more noticeable vibrato. (Although all are slight variations on the same technique). The style or period of a certain piece may also affect the style of vibrato I opt for.
The actual technique of the vibrato might vary depending on your playing style, (or way of finding the notes in the field). If my memory is correct, in the demo that comes with the Moog E-Standard Lydia Kavina moves her hand back/forwards towards the antenna (to play), and her vibrato is sideways, at right angles to her movement through the note field, (not unlike Gordon's fantastic pencil-shading explanation). Others, who move through the note field to and fro in a sweeping sideways arc, would probably do their vibrato at right-angles to this by moving their hand forwards/backwads slightly, (like preparing to through a dart). In short, you can't easily mix and match; your vibrato method needs to "fit" your style of play. Which is why Peter Pringle's advice "to follow the example of a thereminist who has most inspired you. Imitate that person's approach and method as closely as you can until your own style emerges" is so spot on.
All of PP's advice is excellent. At risk of being presumptious, though, I will just add that while you should not try to ride two horses, it's worth having a good wander around the stable before chosing your mount - and, once you're riding, if things don't feel right, don't be afraid to start over if you're certain the first horse you picked was the wrong one! Early on, I opted for a playing-style used by a player I admired, but after a short while I realised it neither suited the music I wanted to play nor comfortably allowed for an old injry of my right hand, so I started over ... and I'm glad I did, because I then tried a method that seemed to suit me much better.
I'll also just add that, personally, I think that you can learn as much watching the inexperienced Youtube thereminists, as the truly excellent ones. If you watch something that, to you, doesn't sound right, it's just as worthwhile looking closely to work out what the player is doing that you'll want to avoid, as it is to observe and replicate the good habits of those whose performance you admire.