Is it permissible to use an eyelash curler to curl eyelashes without chemicals outside the home, knowing that it does not prevent water from reaching the skin during Wudu and no mascara or makeup is applied afterwards?

If the nose clip does not prevent water from reaching the skin, then it is permissible, as it is a common beautification tool like kohl and henna. It is permissible to adorn oneself with it at home or among women, but it is forbidden to adorn oneself with it in front of men to attract their attention.