The PICaxe USB cable is just a USB-Serial Converter. Like a lot of USB-Serial converters, it's based on the FTDI 232 chip. This means you can use most FTDI based converters to program the PICaxe with just few simple modifications;
On the Pixter X, there are headers to make this super easy. If you're using another board, you'll want to connect the USB-Serial cable at the same point in your circuit where you'd connect the TRS jack.
You'll also need to make one small change to the FTDI chip. Here's how;
1 Connect the cable to your PICaxe and to your computer, then download and run FTProg (here). FTProg is FTDI's utility to re-configure their chips.
2 Unzip FTProg, and run FT_PROG.exe. Select Devices >> Scan and Parse, or just hit F5.
3 Your device will show up in the device tree. click the + next to Hardware_Specific, then click on Invert_RS232_Signals. Check the first 4 properties;
Invert TXD
Invert RXD
Invert RTS#
Invert CTS#
4 Click Devices >> Program or just hit CTRL + P
5 The Program Devices Dialog will appear. Check the device to program, then click Program. It will only take a second or two
6 Unplug your usb cable, then plug it back in. Open up the PICaxe programming editor, select the COM port and select the right PICaxe and you're done!