Alfa 1000mW USB adapter in the past (2006 to 2008) came with a USB Y cable (that has two connectors):
The dual lead USB cables were included in the past only to provide electric power for old laptops from the 1990s. The dual USB cable had nothing to do with Tx/Rx output.
Old laptops/notebooks from the 1990s do not support full USB power such as 3.3V 1A. New notebooks have full support so, it’s no problem to use only one USB connectors on the cable (if using the Y-type USB cable, you can use only the larger of the two USB plugs).
If your notebook is old: If you want full output power, better to use 2 USB connector.