Couple of things.
You will need an adapter for switching the nano SIM card from the iPhone 5 to the HTC One. Otherwise you will have to either get customer service to reactivate the other SIM card or get a new one at least twice a week.
He will need to setup his voicemail every single time he switches between the two phones. Apple uses a different voicemail system then all the other phones on the Verizon Wireless network. Switch from the Android to iPhone setup the voicemail. Switch from the iPhone to the Android phone setup the voicemail again. Rinse and repeat. Also any saved voicemails in either system will be lost during every switch.
Finally you can only switch between phone for a total of four times within a billing cycle. After the fourth time, he would be stuck with whichever phone was last activated until the billing cycle resets. The situation you describe is going to involve switching the phone more than four times in a month.