First, you should try to locate the case using FindMy. Have you tried that?
I would be cautious in purchasing a third party replacement case since the functionality of the case in not only charging the AirPods, but also in resetting them and synching the AirPods, is important in maintaining all of the functions of the AirPods themselves.
It looks like Amazon has a few different replacements that they are offering, typically selling for $35 or so. Reviews are mixed, some claiming the cases work fine, others just the opposite.
Alternatively, you can purchase a replacement case from Apple, and you won't need to worry about those things. And if there are problems, then Apple will support resolving them.
It will be more expensive, but that would be my recommendation.
All of the details can be found here:
Need to repair your AirPods? See your service options, their costs by coverage type, and how long they take.
support.apple.com