No a bowl of water does nothing. THere is nothing that you can buy for somthing as small as a cooler or wine frig to create that humidity. You meant you have a small wine frig, right not a cooler like Igloo?
I am working on small humidifiers that are adjustble from 30-90% for sale on my website see my signature below. It's not on there now but will be $100, so not cheap, but the parts aren't either. Anyway, just informing not here to sell.
A bowl does nothing. If you spray distilled water on the walls of the vessel a couple times a day you should be good, but that's something you have to do everyday. You can try taking the bowl and setting it up high and using paper towels laying over the edge of the bowl, half in half out. When put in the water it will wick up the water and create more surface area and you should be good. If it works and goes high then you can vary the amount of paper towels to adjust it.