Open it up - nothing to lose right?
If the power cord rubs against a thin piece of metal or any sort of sharp edge when oscillating, it's the type that can definitely short out and potentially start a fire.
You can ensure the cord has some additional slack and cover up anything it rubs against or secure the cord in some way to avoid the wear-n-tear that eventually damages it, then it's fine to use.
I stopped using the oscillation to be 100% safe. More than 1 brand had this problem. Whatever you buy, definitely scan the product comments for this sort of complaint.