Do any online credit-card gateways pass transaction fees directly to the customer instead of the merchant?

Not in the traditional sense. You can charge the end buyer the fees for CC processing on top of the price of the product/service they are buying, provided that would be okay with them. Many merchants in South Asia and South East Asia do this. Its called "Credit card price", which is different from the "Cash" price.

However, the relationship you have with your credit card payment processor, you would have to pay the fees to them. So whether you get the fees by charging over the top, or subtract it from the selling price, is inconsequential to the payment processor.

The fees still needs to be paid to them and the only logical way of paying them is by charging them (via you).