In China, you can get a pre-paid plan. The offerings change lot, so I suggest checking at a phone store and seeing what options from China Mobile, China Telecom, or China Unicom fit your "secret phone" plan the best. ALL numbers in China are now registered to IDs, so bring your passport. So, if your wife storms the carrier's office waiving your passport around, someone might cave in and let her know about it. On the other hand, if there's a carrier that NONE of your phones (or even your home internet is on), it may be worth a little more each month to use that, since your wife won't have a pre-established account there that might somehow be connected to your primary number already.
Some plans come with phones, others don't. Most "with phone" plans I've seen in China are monthly billing. On the other hand, the carriers are always trying new marketing gimmicks.
Where to get either or both? Simple - Phone stores are VERY common and many would offer plans from more than one carrier. Or, if you already have a preference for a carrier, they also have customer service places that also have phones for sale.
Personally, if I had this issue, I'd first find a low-cost phone with all the features I'd need from a shop in a neigborhood far from my home. Then I'd find an acceptable low-cost prepaid plan to go with it from a carrier that doesn't tie to any current phone, TV, or internet plans used at home. Using this approach should reduce the chances of your wife catching you, unless she reads this thread.
I leave where and how you hide the secret phone up to you. Just realize that if she finds out that it exists, she'll likely do terrible things to you.
Oh, and in other phone related horror stories, my wife was at a small shop yesterday and the shopkeeper's daughter proudly showed off how she had recently added an app to her father's phone that let her listen to his phone at any time, even when he wasn't using it. Such software is of course stongly against all local regulations, and is also likely to come with other security issues both on the altered phone and the one listening in, but it is available. You may want to start your journey at a reliable phone repair shop with your current phone's battery already removed. Ask to have your phone checked to make certain your wife doesn't already have tracking/monitoring/listening software already set up on your phone. If she does, you need to decide if you want it removed (informing her that you know about it) vs leaving it active, but having ways to temporarily disable it (such as battery removal or leaving the phone in a secure location when you want privacy). Otherwise, if such software is installed, she may find out all about your efforts to get a new phone and number before you've even completed the purchase.
You may say to yourself "She'd never install that sort of malware." but at some point, you also didn't realize that she would take your phone and edit your contacts.