Hi Dougal,
Not sure about the CDTV keyboard, it may be a minature din plug instead if the standard din on the 4000, in which case you would need a H/W convertor.
DONT us a PC keyboard altough the plug may fit the electronics aare not compatible, you will need to find a dongle on Ebay etc to convert PC/Amiga.
Good luck with your 4000
PS Check out the state of the internal battery and any surrounding corrosion!
Ian