He may well be a Cockney, Mcc, but is he an etymologist...ie an expert in the history of words? I'm a Scotsman, but I haven't the faintest idea how to play the bagpipes!
Under china, The Oxford English Dictionary - the etymology 'bible' - lists: "short for china plate, rhyming slang for mate". Similarly, under apples, it reads: "rhyming slang for stairs". The point is that the OED does not fight shy of explaining word-meanings by reference to Cockney slang where it applies.
Under peter, for safe, no such rhyming connection is mentioned. If the scholars at the OED have failed to come up with any such link, I'd say it's probable that there isn't one!
Re the fact that peter has meant trunk in any case, as I said earlier, for almost half a millennium...long before rhyming slang appeared...I'd suggest that you think of a trunk standing on its end with the lid open. I'm sure you'll agree that it looks just like...an open safe!
I still believe that peter has nothing to do with rhyming slang.