I have a Swiss watch (which is to say, bought in Switzerland), and it runs on a battery. It’s fortunate that a battery lasts several years, because for the longest time, I could not open it. A watch dealer finally told me it requires a special tool. So I bought my own. Not expensive-- but I wouldn’t have known about it otherwise. I might have tried to force it with a screwdriver or utility blade, and broken it.
If it doesn’t open easily, take it to a jeweler.