Training with a smaller stick is very useful for helping with stick skills and save making. With a short stick, you cannot rely on that extra length of your normal stick to help you make saves or stick tackles and will therefore improve technique.
Training with a short stick is good if you over rely on your stick for saves. Without the added length, you will have to be more pro-active in the way you make saves. With less coverage, you will be forced into bringing your glove across to make the save around your stick; with the extra surface area of the glove to help you block shots. It is especially good for practising making saves with the rhp (right hand glove), rather than trying to block with the stick. As shots come in to your stick side, you can push your right hand out to block with the glove instead.
Using a stick like this is also useful for training to extend the stick out. With a short stick, you will have to play with it in extension if you want to make a good tackle. Practise letting go of your grip and sliding your hand down the stick to grip the end of the stick, so that you have the full length to use. Once done, you can then slide your hand back up (at some point I will write an article about the technique of extending the stick!).
At training, you can practise with your shortened stick; replacing it with your normal stick. Take it to training with you and use it the whole session. Focus on making the save without the stick and using the stick only to help you balance within your ready stance.
Where to get one?
Short sticks are fairly easy to get hold of. If you want to play with a short stick permanently, then you should be able to order a goalie stick at a short length, like 30 inches. A cheap alternative is to be a child’s stick and play with that, although I’m not sure if it would stand up to a high level of shots!