Connect both drives to the Amiga and copy the files directly.
Connect your Amiga per serial cable to the PC and use monitor programs (NComm, Hyperterm) to transfer files.
Connect your Amiga to the PC per ethernet and use the network to transfer files.
Connect the HDDs to the PC and use WinUAE to copy files or to write them to CD-R.
Connect the CD-R drive to the Amiga.
Use the serial or ethernet connection with AmigaExplorer to transfer files.
Send the files to your mailbox by e-mail and receive the mail when the new hdd is installed.
There are lots of possibilities.
Bye,
Thomas
