How about Bitcoin ATM's ? you can withdraw your BTC anonymously. Dont know about the process but you can try.
(....)
Does Bitcoin ATM's also buying Bitcoin or you can sell your Bitcoin in some Bitcoin ATM's? I thought it is only for buying Bitcoins.
Btw, for OP. You can also try to use
https://www.bestchange.com/ for that part since BestChange provides some list of exchanges where you can sell or buy Bitcoins. Just always remember to research first or ask for some feedback about some exchanges that you will have your transaction. 10 Bitcoins is a quite large amount, be careful dealing on some random people or services.