Wire wrap male headers or better way

I have a project with 5 16wire cables, each terminated in a IDC socket connector that would normally plug into regular male headers that are soldered to a pcb. I want to use wire wrap for the whole project and if I stay with the IDC connectors, I need male headers for wire wrap. I have looked for these and found none. So, I suspect my approach is wrong and I should be doing it differently. I do not want to lose the ability to plug/unplug the cables to the circuit board where I'm using wire wrap. For reference, the connector I'm referring to is Jameco part no 119467 which can be seen at jameco.com.

Extended-length pin headers work fine for wire wrapping (http://www.pololu.com/catalog/product/1065 or similar), just push the pin through, solder it in for mechanical stability, and wrap around the extra length.

Excellent thanks very much.

I have used wirewrap socket strips also, longer pins that can be wirewrapped to and then hav e pololu's male terminated crimp pins slid onto for board to board and board to panel connectors. http://www.marcospecialties.com/product.asp?ic=SIP20L You can see a field of them on the vertical board here where the signals from a MAX7221 were broken out to go to 8 widely spaced digits, and one can see the multicolored cables are plugged onto the backs of more of them. The LEDs were soldered in place and wirewrapped directly onto. Only 1 LED did not work and had to be replaced (overheated most likely). A duemilanove is temporarily wired in after a loose wire smoked a promini.