I soak mine for about 30 minutes. When mine have scale infections or anything of that nature I do it once a night until its gone. Which is usually its next shed.
But what I do is I take a big rubbermaid and sit it in my bathtub. Fill the rubbermaid up with warm water. Poor the betadine solution in it and then sit the snake in it close the top and leave them. My snakes are so big I cant just leave them in the tub becuase they jump right out so I have to use a rubbermaid. If your snakes not that big you can just fill your tub up and put it in there.
Also if you go to cvs or your local pharmacy. You can pick up something called zinc oxide and put that on him also.
So the betadine is not harmful if it gets in his nose or mouth?, I'll just fill his big shoebox with solution right in his cage and I'll leave it everyday for half hour. This guy loves to swim in water and that's part of his problem now.