You are probably right. I found out I have to go to the hospital for neck surgery next week, I'll have to deal with Apple when I get back.
Certainly in no position to fix it myself at this point in time.
From what i've seen in youtube videos though changing batteries is do-able just a little tricky...
On an iPad? Like I said, my understanding is that this is notoriously difficult because you have to deal with lots of hardened glue. iFixit sells some purpose-made product to soften the glue, but based on the cost and overall difficulty, IMO it's really meant for professional service providers than DIYers.
As far as the question about Apple refurbished products, everyone says these are "like new." My gf and I recently went in for the iPhone battery swap... 90 minutes later, they said the original device was bricked so they gave her a pristine refurbished unit. Unlike third party providers, Apple has strict customer data policies so I wouldn't even worry about doing a full wipe (i.e. factory reset) before turning the unit in. Obviously you should make a full iTunes backup (or at least an iCloud backup).
Personally I keep most of my electronics in excellent condition but most consumers will not receive an Apple refurbished device any worse than their current unit.
And hope the procedure went well!