I wouldn't imagine there'd be any need to call CS, just pop your SIM into the new phone (assuming it's a nano SIM (or you can cut it down)) and turn it on. The only thing that needs activating via CS is the new nano SIM that comes inside the M8, if you're using your original SIM then there shouldn't be anything to call CS about.
The above only applies if both phones and lines are using LTE phones with SIM cards, if they're still on 3G phones with no SIM, then you'll need CS to switch lines and phones around.
Verizon HTC One (M8)
Verizon Samsung Galaxy S4 (SCH-I545)