I want to set up a security camera at a cottage that has no internet. I need to record and store events for up to 4-6 months at a time without requiring internet access. Would Wyze Cam work for this?
In order to setup the camera on your account, you would need to have an internet connection. But once it is setup and you configure your SD Card, you should be ok, but not able to access it until you come to retrieve the card. You can use larger SD Cards now, but would make sure it is a high speed card and then either do continuous or event recordings. I am not sure on what the size of the card should be given the amount of events being captured.
Which camera are you talking about?
In any event, I would test this with the type of camera you are looking at using (Verification is key). Attach it to your network and if you router permits, block internet after it is configured. Let it run for a day or so and then pull the SD Card from it and see if it recorded anything. Or connect it back to your network and take a look at the playback and see if it successfully recorded. If test was a success, then go install it.
A V2 or V3 camera will record without Internet, but they MUST have Internet to boot up. So the biggest problems you will have are 1) Starting the camera with Internet, and 2) Making sure power never goes down.
If you have a Wyze Outdoor Camera, you can set it up to run without Internet in travel mode. But then the question becomes how is it powered? The battery may last 4-6 months without any trips, but the more trips the shorter the battery life. Powering it is cool indoors, but outdoors you need a sealed connector to keep it from getting flooded with water.
So what may be the biggest question of all, is what is your end game? If security, the camera may also be stolen, and it wasn’t able to report the theft because of no Internet. So maybe you hide it in a tree to capture the license plate of the thief, but then you need to power it. A solar panel may work if in a tree for the Outdoor camera, if it has access to the Sun (questionable). You see where I am going – think about what you are after and how you will accomplish it. 
So I guess a lot more details?
This is the deal breaker. So no, Wyze cameras are NOT a good choice for this usage.
One workaround is leaving a mobile 4G hotspot at the cottage.