USBasp progarammer with ZIF socket?
You can replace the 10-pin ISP socket with a 6-pin ISP socket, they are functionally identical.

The original USBASP design brings out an additional 2 signals (the TX and RX pin of the programmer MCU) to normally unused pins of the ISP-10 connector because the USBASP creator planned to add support for access to the target UART for debugging to the firmware, but this was never implemented. You definitely don't need these pins for programming.

I don't think it would be very useful to have these two signals on an ISP-10 header anyway, as most devices with an ISP-10 connector will have these pins connected to ground.