I'm short and have small hands and fly with index&thumb........... On the right stick.

And sometimes thumb, sometimes index&thumb on the left stick.

I can hold the TX quite securely too. Have used a neck strap back when I flew a lot of slope and thermal. Now that I'm flying glofuel all the time now, I don't use the strap as it requires too much looking out for while starting and is more bother than value to me.

The issue in this thread that bothers me is the idea that the flight instructor is pushing his student to use one method or the other. I really don't believe forcing anyone into what is basically a technique. If I were you and your instructor was adamant about how you hold the TX and went farther on that issue than just making a suggestion and giving his reasons, I'd find another instructor. There's something akilter with that old boy. He may be the best at your field, but I'd bet he's far from it. Most who're that narrowed on an issue are usually prejudiced more than they're knowledgable about most everything. Look around. There are a lot smarter ones around.