no id will be your stumbling block, even localbitcoins wants it most of them time.
take a look at bitsquare.io. that's p2p and decentralised. i don't know if there are premiums on there.
forget cards for whatever you're planning.
I've done quite a few btc->fiat transactions on there and I can tell you that the system bitsquare has is legit. The only "premiums" that come from using that exchange platform is from other peers setting it that high. What drives down the costs are purely from competition and how badly you want to sell/buy.
I've also done a few transactions on localbitcoins as well, and the same goes for ID's... it's basically the person selling the bitcoins gets to decide how much info he wants from you to determine if you are trust worthy to sell too, as well as other things to consider, like taking pictures of receipts if you are depositing cash with a cash deposit to their bank account, etc.
Edit: what's great about bitsquare, is that there really isn't a need to talk to the other person at all really... so the ability for a seller to require an ID to trade is non existent.