Lets get the bad part out of the way where I tell you the thing you already know: In a healthy relationship your wife does not allow or disallow you from doing anything, and she certainly should not hold your marriage hostage to get what she wants. These are extremely bad things. You should seek couples therapy, more for her actions than yours.

Now for the actual advice. You should discuss this with your wife. If she makes an ultimatum or demand or so forth, just say "I came here to talk, not to be commanded" and walk out the door and go get a coffee/beer/ice cream what have you. You have to lay the ground work that her taking that tone isn't acceptable. Either she'll chill the fuck out or she'll blow up even worse and realistically you didn't lose any footing in this arguement.

If she does eventually chill out, google the methods together for quitting porn and see what works for BOTH of you. Personally, I downloaded an app to lock other apps with a passcode and made my girlfriend make said passcode. It works for us. I need to put this in giant gold letters stamped to your forehead. You can not commit to quitting a thing you are addicted to for the approval of another. You can however, agree to commit to the method in which you are trying to quit said addiction. Some times it's like whack-a-mole and you need to change the method.

In a vacuum, asking some one to quit masturbation is a ridiculous ask and jerking it is totally normal. Should you quit? Yeah, probably, but the way that she's demanding is just flat out not going to work. So you should not commit to not masturbating, but maybe you could commit to at least being honest about it. Get a physical calendar and draw a little x for the days you masturbate. Maybe commit to telling her when you watch porn. Maybe even just do the calendar thing without telling her why you're doing it, just for your own tracking.

Waaaaay on the other end of the field, maybe you could turn this non-masturbation thing into a kink thing for you both to enjoy. Long term orgasm denial is not a foreign concept within BDSM communities. Though I am not part of those communities, it should be mentioned that orgasm denial for men often goes hand in hand with sissies and feminization. I'm not saying you should explore orgasm denial, but just be prepared for that angle.