Personally, what I would be hesitant about is giving the broker a „wrong“ TIN - or making stuff up like giving a foreign one. That sounds like a „quick fix“ but might bring up issues or consequences later.
The brokers will be able to look up the expected number format for countries (and in many countries it is not the social security number) and be able to notice that it does not match the country of residence as stated by the customer.
As far as I know (and I have at least skimmed through them, the OECD AEOI) framework does provide for situations where the holder of a reportable account does not have and cannot provide a TIN - and the reporting entity has to be able to state the reason for that.
I have had to explain this it to a European bank of mine, at the time when Switzerland hadn‘t formally defined a TIN (for natural persons) for AEOI purposes. They kept pressing me about it though, even inquiring my VAT no. - which made no sense, because as a natural person I didn‘t have one. In the end, it was resolved by „provisionally“ giving them my AVS number, after I had found out that Switzerland was about use that (though the law wasn‘t in force back then, so legally I still had none).
Basically, even though it was a fairly international bank, they didn‘t quite know what to do and how to handle that.
In the case of you people without Swiss TIN, despite being resident in Switzerland, I would maybe try to explain the situation to them, clearly pointing them to the legal grounds (not being insured by Swiss AVS/AHV on which legal basis, due to working for international orgnization) and maybe provide documentation of having asked the local tax office (or their answer in writing).
Still, the looming question may be what they‘re going to do with it. Accept it for what it is?
I would expect: the more knowledgable the person handling your case is about international taxation, tax laws and AEOI process, the more likely they are going to accept that „exception“ from the rule („every customer has to provide TIN“) and internal documentation („customer has to be able to do so, if it‘s in our internal documentation“). The less, the more likely they are going to throw you out.
