I am sure your hamster will be fine, as long as he is dry now.
Until you can replace the bottle have you got a small tea light bowl or something similar you can put soem water in?
I personally have never had a problem with these bottles
https://www.petsathome.com/shop/en/p...e-water-bottle
or you can get a more expensive glass one like;
https://smile.amazon.co.uk/gp/produc...?ie=UTF8&psc=1
pets at home also do a glass version, but I have never personally used one. (Not sure which country you are in)