I agree, you definitely should be using polo wraps on all four of your horses legs if you are going to be playing around and stick-n-balling. Also, you you cannot make your own mallet but I would see if you could borrow or try one out from somebody else before buying your own. They come in different sizes and the one that's right for you can vary based on your body, your horses body, and your natural ability to bend and reach down for the ball.
If you are planning on teaching your pony to stick and ball, first make sure that your horse is already comfortable with neck reining. A little help with your leg is alright, but you need to make sure your right hand is completely free for the mallet. Secondly, many times horses can become quite nervous around the mallets and polo balls (especially because of the loud sound that you'll make when you hit the ball!) so make sure your pony is used to it. I've seen some trainers even begin by hanging polo mallets in their horse's stall! Once you finally decide to get on with the mallet, just walk around and swing it, not even going for the ball. Make sure your horse gets used to you swinging it on both of it's sides, (you hold the mallet in your right hand and your right side is called the offside, while your left side is called the nearside) in front of its legs, and behind it a bit, just so there are no surprises when you actually hit the ball. Start off nice and slow, and move your way up. It may take weeks before your horse is comfortable enough for you to hit the ball, but be patient.. polo can be scary, but once their comfortable, horses tend to really love it can be a great way for you to bond with you pony!
Good luck finding a club in New Zealand! Have Fun!