Is it possible to use a Verizon CDMA iPhone 4 with any other carrier or Pay-Per-Use carrier?
Not likely unless Verizon agrees to release that phone for another carrier. Have a look at this guide on identifying iPhone models:


Identifying iPhone models


The iPhone 4 you have is model A1349 (that should be printed on the back of the device), and if so, it is a pure CDMA phone so you cannot connect it to a GSM carrier due to differing radio technology.

Even if you were to jailbreak it or get Verizon to unlock it, it's only going to work with another CDMA carrier.

So in the USA - you need to find a carrier with coverage in CDMA EV-DO Rev. A (800, 1900 MHz) and that's primarily Sprint and Verizon. Since there is no SIM card in this device, you might not need to get it unlocked, but that will be a dialog between you and your potential carrier if they can provide coverage to it at the same time as Verizon may have it registered as "their locked device"

Due to bilateral roaming agreements - each CDMA tower in the US can and does serve multiple carrier devices - so it's likely that Verizon could prevent you from using your device on a competing carrier until you fulfilled your contract or convinced them to release that device's status in the common database for cell phones.

There are well over 50 regional and national carriers providing CDMA coverage according to this wikipedia article so you might have considerable options in some regions of the US. 

Nore some of the information is old due to consolidation. Your main bets are C Spire, Sprint and Verizon.