I would get a long enough cable with a female 3.5 mm jack at one end and a 3.5 mm plug at the other end. You can still use the screw-on adaptor to go to the 6.3 mm jack into your new audio card. To reduce losses through the cable and not increase the impedance much, get the wire gauge for the extension cable to be a lower number (larger diameter wire) than your existing headphone cable.