Before learning so much about iodine, we've always used grapefruit seed extract for throat issues. It tastes even nastier than Iodine in water, but seems to take care of the problem quickly.
You might have him gargle with the Iodine in water so it spends more time in the tonsil area than when he just swallows. Probably just me, but the thought of actually touching an Iodine covered swab to the back of my throat creates an instant gag reflex. ;)
You might also find other nutritional support for his immune system.