Hiya,
i use bowls for all of my hamster, Syrians and Robos, and unfortunately that is just something i need to do every day for most of them - empty and replace the water bowl!! I know this is very time consuming, and sometimes i need to do it 2 or 3 times a day, especially for the ones which like the dig!!
You could try using one of the 'sippy' bottles - i think that is what they are called - they stick to the cage (inside or outside) with suckers - but it just depends how interested you hamster is with it, as it might pull it down if it pays too much attention to it!
Does the cage not have a shelf? could you not put the bowl on the shelf and put no shavings or bedding on the shelf so there is nothing to fill it up?
Let us know how you get on
Good Luck,
Tammy x