- You don't have a choice.
- It depends, but the options are "no form" or 1099-MISC. You'll never send a 1099-K.
The only 1099 you would potentially be required to send for business payments is a 1099-MISC. The IRS instructions on that are pretty clear as to when and how you must use that.
Note that you don't send 1099-K's unless you are a payment settlement entity. Furthermore, if you transmit the funds using a payment settlement entity who will report the transaction on a 1099-K, then you don't need to report it on a 1099-MISC. (See "Form 1099-K" ibid.)
Fortunately, PayPal is a payment settlement entity, so you don't need to worry about reporting payments you send through them ... with one big exception: PayPal does not report "payments to friends and family," and so if you're using that to avoid their fees then the IRS would consider you liable for reporting payments on a 1099-MISC. To my knowledge banks do not report wire transfers, so you would have to file 1099-MISC when required for payments sent that way.
Regarding your TIN: Yes, these numbers get circulated in the course of business. But this is actually one of the few legal uses of those numbers, and it's required, so if you're worried about identity theft or something then buy insurance against that. And if you think you've got it bad, just think how your payment recipient must feel: Before you send funds that would need to be reported next year you are supposed to demand a signed W-9 from them (so that you can make the report). But hey, the IRS isn't oblivious to your concern: Check their "helpful" advice on the last page of W-9 to "Secure Your Tax Records from Identity Theft."
Regarding payments to entities not subject to U.S. taxation: You don't have to report those, and the fact that you reasonably believe the entity to be foreign is considered adequate to omit them from your 1099-MISC filings.