Since it's currently registered to your account, there will be no problem in unregistering it and re-registering it.
It's nowhere near old enough to cause a problem - some older Kindles needed an update to their security keys before they could be registered, I think. And the Kindle 1 and 2 didn't have wifi, and their 2G connections are not supported anymore. None of that applies to an Oasis.
Lovely model the Oasis. I recently got an Oasis 10th Gen with 4G. Second-hand, of course.
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