I have worked out an answer for you below ...
1. The fact he has now swallowed the rawhide it is good, these are natural products and the digestive juices in the stomach are capable of partially digesting it and softening it so the chances are it will just pass, so for present all you need do is to monitor your dog, you may expect to see a mild transient bout of indigestion over the next few hours but in most cases I would not expect to see worse than that.
2. However in a minority of case more severe symptoms could occur as a result of intestinal tract obstruction which can be a very serious situation. So if more serious symptoms occur such as lethargy, inappetance, vomiting, straining or signs of abdominal pain then you should have your dog checked over by a vet without delay.
In my experience most dog will come through this sort of incident without problem, but keep a good eye on your dog anyway ...
I hope I have covered your question fully enough but if you would like further clarification or to talk things over a bit more then I will be on-line for the next hour or so and I will be more than pleased to continue working with you.
Please be kind enough to rate my service to you after we have concluded our dialogue, such feedback helps me maintain the quality of my answers.