I think this is absolutely the way to proceed.

Unfortunately at a restaurant in Wengen, Switzerland, the waitress seemed baffled when I told her to negate the US-Dollar charge she had run and re-run it in CHF. She kept saying "It's not possible." I signed and asked to see the hotel manager on my way out the door (he had earlier stopped by the table to introduce himself). He reversed that original charge without question and re-ran it in CHF. In this particular case I had specifically asked the waitress to verify that the original charge would be in Francs, so I got a bit heated when it showed up in dollars.

The manager seemed not to be aware of US card issuers charging a fee even when the charge is processed in dollars - this may have been part of the issue - but the hotel's converted amount was 3% above the official rate.

I was afraid that I'd be hit with a fee for each transaction (original charge, backing out the original charge, the charge run in the correct currency) but luckily for me it was a CapitalOne card and so there was never a foreign transaction fee for any transaction. I don't know how other banks would handle the reversal - is the fee reversed, or is it charged a second (and third) time?