Amethyste,
Pay no attention to what others are telling you. Look deep into my eyes, and listen only to my voice. All other sounds are fading into nothing and only the sound of my voice remains.........etc. etc.
Tiny hands with cocktail sausage fingers are no problem. You can still use a Rockmore style "aerial fingering" technique but instead of using four positions you will use only three. Position one is with the fingers nestled in the palm of the hand, in position two the fingers are fanned slightly forward toward the pitch antenna, and in position three they are fully extended.
What you must understand is that playing the theremin is essentially an intuitive thing and since everyone is constructed differently you must adapt (like the Borg).
A simple major scale would be played with the following hand positions 1-2-3-1-2-3-1-2, rather than 1-2-3-4-1-2-3-4.
What you must not do is get discouraged and start using some technique of your own devising. It might seem much better to begin with and sound like you are getting results, but in the long run it would most likely be defeating.
BTW, Clara was tiny and had freakishly long fingers that were curiously double jointed. Many people have suggested that this accounted for her uncanny ability on the theremin. I do not believe that. I think it was because she worked so hard to overcome the problems she had, that she developed such extraordinary facility. Don't forget, it was because of a disability of her right arm and hand (her bowing arm) that she had to abandon the violin in 1930 and take up the theremin in the first place.
Violinist Itzhak Perlman once said that the difficulty of any musical instrument can be judged by how long it takes a beginner to learn to play a simple melody on it accurately and consistently.
"The theremin is the most difficult of all instruments. It's much harder than the violin, which I played for years." Clara Rockmore
Many singers come to the theremin and think they are going to be able to play it quite easily because the instrument sounds like a singer and singing is something they can already do. There is a period of shock (I know because I went through it) that can last anywhere from a few days to a few weeks. This is a dangerous time because it is so easy to get discouraged and decide you have made a mistake in deciding to take up the theremin in the first place.
Suddenly you're a singer who is singing off key!
Stick with it and all that will eventually straighten out. When it does, you will find that playing the theremin, although it is a constant challenge, is profoundly rewarding and satisfying.