Erase broken iPhone or remove from iCloud for resale?

I have just sold my son's iPhone 6S on eBay. The screen is smashed and has stopped responding to touch. He had switched off mobile data at the time. When switched on, the passcode screen comes up, but the phone does not connect to our home wifi... not sure if this is because the passcode screen is there.

My question is whether I should erase the phone via Find my iphone on icloud and the remove from iCloud or just go straight for simply removing the device from the account. Buyer is suggesting I do the latter.

What will happen when the phone is repaired? Will either of the above actions work given there is no internet connection? Would the new user be able to connect to a new wifi network? Will they be given the chance to join a new network so that remote erase and removal from iCloud will work?