This is kind of a tough one. We do have short codes you can use to change the way your phone forwards calls but it's an all or nothing kind of thing. What I mean is that we have a forwarding option (available to eligible postpaid plans) that will forward all your calls to a number that you set and your phone will not ring at all. In theory, you can set all your calls to forward to a dead random number like 15555555555 and when people call your primary number, those calls will immediately be forwarded to that fake number. You will not get a notification of a missed call nor any voicemail messages as the calls are going straight to that fake number and never touching your phone.
If you want to set this unconditional call forwarding you can follow these steps
**21*PhoneNumber# Turn on unconditional forwarding (CFU) to a number. ##21# Turn off unconditional forwarding.
If travelling internationally, will this avoid charges for voicemail?