You never told me your secrets
Why can't you tell me how your product works?
Is it because you are in "stealth mode"?
Your idea, isn't worth a damn thing until it's executing in a product, until it has shipped to your customer. You can't grow your idea if you don't share it.
Product managers keep secrets for two reasons.
1) because it's imperative to their product's success
2) because before they had successes they tried lots of things that didn't work (and they realize they didn't learn anything that customers care about now)
If your product idea isn't very good you won't be able to figure out how to execute. Hiring a different product manager won't help you with that.
Instead of telling me you'r busy figuring out your product, that you are in stealth mode, how about you ship? Show me that someone considers your vision valuable enough to pay for.
Your idea, your vision, is never going to get "stolen" if it's only expressed as an idea, as a proposal, as a pro forma. It is not worth anything if you can't ship it and get customers.
Product Mangers can give you good advice, they will sign your NDA and in my experience they all honor it. They certainly won't tell anyone about your product, if they don't understand how your product works.