So I went to my bank to get the information Hyatt was requesting in order to do the refund. As soon as I explained the situation to my bank, they advised me AGAINST providing anyone (especially overseas) with bank account, ABBA, and swift numbers as this information can be used to clear your account from any funds at a future date. The fact that you might have very little money in the account doesn't prevent anyone from withdrawing more as your account can go 'negative'. Bank manager explained that in case of fraud, the amount of paperwork you would have to fill out is massive. Plus there are no guarantees someone might not try to sell the info on the black market.
When I got back to my office I contacted Chase and they informed me there is no way the hotel's accounting department could have attempted to credit my credit card account and they would reject it, nor did they see any attempts made to credit the account. At that point, they referred me to their disputes department; after explaining the situation Chase will credit my account and they'll take it up with the vendor directly.
This is the first and last time I'm leaving a hotel without validating the charges at the desk before I leave. Lesson learned...