I'm getting confused a little when reading your message, but I think your question is if you take your son's upgrade, will you still have to pay for data? If your device is a smartphone you will have to pay for data, that is required. If you have a feature phone, you won't be REQUIRED to have any data package at all, unless you have an older "3G Multimedia" device with the requirement.
Also, you are not switching lines by transferring upgrades. You won't be "taking over" as you say really. By giving your son your upgrade, your contract is extended, not his. When his upgrade comes, you will be doing the same, extending his contract, and just using the phone his upgrade gets.
Hope that helps.
There are several things to consider here.
1) Here is how a "buddy upgrade" works: The line that is eligible signs a new 2-year contract and purchases a subsidized phone. Then, that phone is activated on another line on the account. The new contract stays with the line that was eligible, and you do not have to change the primary line or any of that. If the eligible line has a New Every 2 credit available, then it can use it for the upgrade.
2) The New Every 2 credit (the $30 or $50 discount a primary line gets on top of the subsidized pricing for a new phone when signing a contract) can ONLY be used through Verizon. It cannot be used on Wirefly or another third-party retailer. You should also note that this program has been discontinued, so it is the last NE2 credit you will be able to use.
3) When you upgrade through a 3rd party retailer like Wirefly, most of the time you agree to keep the phone active on the line it was purchased on with the plan you chose for 6 months. Read the second contract that they make you sign. If you transfer the new phone to your son's line after purchasing through them, you may incur an ETF from Wirefly (that has nothing to do with your Verizon contract).
Since you want to swap upgrades, I would go directly through Verizon. Either on this website, or at a corporate store. That way, you can use your NE2 credit, and you will have the flexibility to swap phones to different lines as you like without worrying about any penalties.