It might be worth doing a few minutes’ online research to see if you can find out what it’s made from (maybe injection-moulded polystyrene, or PVC, or acrylic ?). The way it’s disintegrated looks like it might have been embrittled by age and/or exposure to sunlight. Some plastics can be affected by solvents in fillers.
If it was worth really serious money then the best advice would usually be to sell it, just as it is, to a specialist restorer rather than risk doing anything irreversibly bad to it. But if you want to keep it, or reckon it’s not worth a great deal in any case, then a DIY fix might well be fine. I assume any light inside wouldn’t reach down the arm to the hand. If it would then it would back-light any repair which would reveal it in all its subtlety or otherwise.
Please take it to these people with your flies undone and tell them it survived for 50 years before you got your hands on then it all went wrong. When they’ve restored it and you’ve made TV gold, drop it again on the way out the door.