A number of rather dated discussions here suggest a phone owner can do this him/herself. In my experience with a new S7 as of October 2017, the menu options described no longer exist. It seems to be necessary to call and 'mother may I' the feature off.
While I as a customer would prefer to be able to remove Visual Voice Mail without divine intervention, my experience suggests that this is no longer possible. I recommend you just call and stay on the line (or chat or whatever) until the rep thinks it is off and you verify you can ring your cell phone and process a voice mail w/o that "Subscribe to VVM" nonsense. Good luck.
Once you have the Block Visual Voicemail feature on your line, it is listed under "Service Blocks" section of your MyVerizon account online.
I'm most definitely NOT a VZW employee. If a post answered your question, please mark it as the answer.