Your best bet would probably LocalBitcoins[1]. Using their service you can look for buyers/sellers in your city so you can do bank transfers without those KYC on exchanges, or maybe even pay or receive money via cash. Check it out.
[1] https://localbitcoins.com/
But I think it is not a big problem to send our picture to someone since we all are using social media like facebook and instagram we all are uploading our picture and all other information too.So for me it is not a big matter to show my proof to anyone.