Judging by this, I would suggest a merchant account would be the best way to handle this, with the initial and final transactions being tagged as bank transfers to the original and final accounts.
However each bank account can only have one currency, so you may find it easier to do everything from your base currency perspective. I also found this topic which may be of some help, but typically a merchant account would be the way to record this.
It may best to clarify this with your bookkeeper or accountant (I’m neither) who should be able to confirm if this is correct in your situation.