Do you know any exchange which accepts fiat money deposits without asking for KYC and AML procedures? I know only virwox but their fees are outrageous...
Have you checked whether there are any viable LocalBitcoins.com traders in your area? Centralized exchanges that do not follow KYC / AML guidelines don't last so long nowadays. Depending on where you are based your local Bitcoin traders may be a bit more flexible (although most now also follow KYC / AML guidelines once certain volumes are reached).
You wont really have any choice but doing either P2P or using up LBC because when we do talk about Fiat deposits then it do always integrate with KYC.