In general, CD-i is a universal compatible standard but it seems there are exceptions: The controllers that work on your CD-i 180 player (the first one built by Kyocera) do not work on other CD-i players, these are specific to this type. Another example, the thumbstick that LG supplied with their CD-i players, does not work on Philips CD-i players. Philips used RC5 and RC6 as IR protocol, over the course of the years, Philips stopped with RC5 and only supported RC6. That's why players that originally came with the large thumbstick can not use the small thumbstick by Philips. But, according to Retrostuff, you can use the RC6 commander on the older players. Next to these examples, we also have an official (wired) CD-i Mouse made by Sony, which they supplied with their CD-i players IVO-10, IVO-11 and IVO-N7 (Sony released three CD-i players on the market). The CD-i Mouse follows the Green Book standard perfectly and it also works on other non-Sony CD-i players.
[Thanks, Rich Pemberton]