From whatever I know; never ever reveal your private key to anyone. That's the foremost rule in crypto. Also avoid keeping your investment in an exchange else you won't be able to redeem these all crypto dividends. You need to just sign a message to register to claim your coins on the their chain. Yes, of course you do have to expose you address and anyone can log your IP address. You could go in a cafe if you are so worried else check out https://www.pcmag.com/article2/0,2817,2403388,00.asp ; I just googled it. You can purchase as per your needs.
Hope that helps.