Lauren:

Thank you for your advice.
I also gave this some thought and figured we can still make the transactions, albeit not in one entry.
I in fact tried this earlier this morning, and figured out that this is the work-around:
We perform a BR transfer between the USD and CAD banks, and then between the CAD and CHF banks.
If we are careful with the rates, we can ensure that the transfer in & out of the CAD bank will net to $0.00.
And in the end, the USD funds will have been transferred to the CHF bank.

I am glad that your input verifies that this is the way to achieve the transaction.