Should there be any problem cooling Mysore Pak outside a refrigerator?
Batters are not shelf stable. It doesn't matter if their ingredients are shelf stable by themselves or not. So you have to follow the basic food safety rules for non-shelf-stable food. In particular, you have to ensure (no matter by what means) that it doesn't spend more than 4 hours with an internal temperature between 4 and 60 degrees Celsius. 

If you can prove that your cooling procedure does that, you are fine. If you don't know, then it is unsafe.