I am wondering how people ask if they can handle a particular item in a shop, to check how it works or look at it more closely.
My guess would be "Can I watch it?" but it is probably not so good.
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You would say something like:
Could I take a look at it, please?
Could I examine it, please?
Whereas 'watch' in this sense would mean to observe something over a period of time, such as watching TV or a football match.