tl;dr on all the answers here, but I'm actually facing the exact same quandary in my own novel. In addition, the secret the MC is keeping (his career) would come up conversationally between himself and the rest of the characters, so it's a constant struggle.
I am employing a number of different tactics.
1. Making the secret a known-unknown to the reader In other words, the reader knows there is a secret, because of the MC's (and exposition's) lack of specificity. By being glaringly obvious that I'm not going to come out and tell them what the MC does, the reader knows that there is a secret to find out, and I can lay breadcrumbs to keep them turning the pages. When I was first concepting the story, this was a sticking point. When I decided, oh wait, this could fun, it became a commodity. It adds a mystique to the MC, and gives the reader something else to look forward to in the book. Plus, it's not a sudden, unprojected surprise.
2. Misdirection I tweaked my concept once I decided to embrace point 1, adding a couple supporting characters, and voila, I have red herrings everywhere. I am intentionally using specific language and situations to suggest to the reader that the MC does X for a living, and I will often write as though X were indeed true. It helps me to embrace the lie, as the MC does (Method Writing? wink) and further obfuscate the truth. When situations arise in which the MC has to actively cover, I don't hide that from the reader, just the characters.
With that in mind, I decided on third-person limited multi-perspective. 846
It allows me to give clues from the MCs POV, and when I'm writing from other characters' POV, I try to fill in the blanks of what the reader might be asking of themselves (wait, if he does X, why would he say that?) and also further misdirection with their own theories of what he does.
1. I sweat a lot Which is to say that this is really fn hard to write. I'm constantly checking my language and phrasing and keeping notes (Scrivener footnotes and thumbtacks are really helpful for this) on what I say and how I say it. Obviously I don't want it to read clunky, and I don't want to disenfranchise my reader, I want to use that mystery as a subplot to draw them into main plotline. So I read and re-read what I write, and I have a brilliant, sexy, red-headed editor to bounce drafts off of.
I might recommend finding a writing circle (Write On, Critique Circle, et al), and doing control experiments. Keep one group in the dark, let the other in on the secret, and then ask each to give you their feedback on how it's progressing. Does this make sense? What do you think the secret might be? How did you come to that conclusion? Is it frustrating or fun? Etc. A potential benefit to this technique is that readers can often come up with wonderful theories that you can employ in the book!
1. Backspace You can use Shft+Left/Right/Up/Down arrow keys to select larger selections of text for deletion. How do I know this little shortcut? I'm using the same tactic! ;)
Did I mention that this is really hard? Don't expect to get it right the first time. But if you can pull it off, it can only add to the story. Cheers. 487