It should be possible for you to pay that with your swiss e-banking.
But are you sure you would want to move your money from US account to Swiss account and then pay US credit cards from the Swiss account?

The Swiss currency is so strong at the moment, that you will probably loose some money doing that. It may be worth considering keeping your US money in US for a while longer.... just a thought
I have not moved my money to CH from my home country as I would loose with the current exchange rate - in addition, there are charges for transferring money internationally, that you may not be paying if you pay your US credit card from US bank account.
Hope you´ll enjoy Switzerland when you get here - Is a great place to be