Anonymously Transferring a Domain To Someone

Several months ago, I registered the domain name for a project my company was working on. It was a spur-of-the-moment decision that I now deeply regret; I’m far more concerned about keeping my job than making a couple bucks.

I received an email a week ago from someone offering to buy the domain, and I want to ensure I can transfer it without ever disclosing my identity. I bought it using the registrar’s proxy service for privacy, but I don’t know how secure that is and if they’ll continue to mask my ownership even after the transfer.

Any advice would be greatly appreciated.