These are the details of the two Internet connection hardware from the connection wizard in Eee 701 original software:
.....................
Description: Atheros Technology Corp. L2 100 Mbit Ethernet Adapter
Device type: PCI
Manufacturer: Atheros Technology Corp
MAC address: 00:1f:c6:7b:1f:fd
Driver: atl2
....................
Description: Atheros Communications, Inc AR5007EG 802.11 b/g Wireless PCI Express Adapter
Device type: PCI
Manufacturer: Atheros Communications, Inc
MAC address: 00:15:af:93:5a:ed
Driver: ath_pci
.................
And also I assume that this one is coming from my phone:
Description: ArkMicroChips USB-UART Controller
Device type: USB
Manufacturer: ArkMicroChips
Driver: ark3116
..............

A search in knoppix for ath_pci gives :
/sys/module/ath_pci/
/sys/bus/pci/drivers/ath_pci
clicking on the sub folders in these directories goes seeming reoccurring on forever.
A search in knoppix for atl2 gives : nothing.

On the storage in EeePC:

Index of file:///mnt/hdc2/lib/modules/2.6.21.4-eeepc/atheros/
Up to higher level directory
File: ath_dfs.ko 34 KB 02/12/08 01:00:53
File: ath_hal.ko 157 KB 02/12/08 01:00:53
File: ath_pci.ko 103 KB 02/12/08 01:00:53
File: ath_rate_atheros.ko 31 KB 02/12/08 01:00:53
File: wlan.ko 211 KB 02/12/08 01:00:53
File: wlan_scan_sta.ko 16 KB 02/12/08 01:00:53

Index of file:///mnt/hdc2/lib/modules/2.6.21.4-eeepc/net
Up to higher level directory
File: atl2.ko 36 KB 09/24/07 15:05:57
So I figure it is a matter of copying the files over to somewhere? in knoppix or altering the script in knoppix to search these directories.
Will wait here for someone who knows how to proceed.