All App Store, iTunes purchases & iCloud data are all linked to the Apple ID, not the device.
As far as I know, you cannot 'delete' an ID from the machine without completely wiping it; or perhaps you could but it would take a lot of digging. You just log out of it, then into your own...
You will either have to keep swapping IDs all the time to access updates & authorise iTunes, re-purchase under you own ID, or set up Family Sharing, which allows all family members to 'own' shared software & music. Use your wife's ID as the 'master' account, as this will preserve most of the existing structure.
iCloud data, contacts keychain passwords etc will possibly have to be recreated from scratch. I've no experience with that, sorry.
To my knowledge, it will still work. But you can't update them. And you can't redownload them (if you happen to delete them). You will need your wife's Apple ID to redownload them. – Darius – 2014-11-13T00:25:53.310