There was apparently an experimental .402 Martini trialed in the 1880's, but these were all full size Martini-henry style rather than the smaller cadet. Seems most were then converted back to
577-450 or .303 as the "small bore" .402 was already becoming obsolete as it was developed.

Would be very interested in pictures, or even chamber cast measurements, but you probably don't have that degree of access to the gun (wish I could add smileys). cadets are fidly to cast anyway, no straight line access.

Many conversions were carried out by a company called "Sportco" in Australia. They generaly added their name and polished many markings off the reciever in the process. All sorts of "odd" chamberings, mine is .22LR, but many .222 rimmed, .22 Hornet, .218 Bee etc exist. Even more wildcats made by individuals.