So here's a question: Why don't you want to lie to them? You don't even have to lie, just tell an incomplete truth. Just tell them something normal, like you're an office worker or manager. That way, you know and they know that they didn't just want you for your money.
Afterwards, if things go well, you can tell them the complete truth, and that would certainly help your cause a great deal at that point ("Oh my god I've been dating a millionaire and I didn't even know it"). If they accuse you of lying, you can just say "Hey, a CEO is an office worker, I didn't lie", which is also true.
I used to have a somewhat similar situation: In my home town, everybody knew me because of some sports medals I had won. (That's probably part of why I became so bad at approaching & meeting girls: I got used to just riding the fame, used to having girls I didn't know get excited when they saw me, which didn't come with me when I left town.) I used to never tell girls (or even guys for that matter) about my international competitions, until after they knew me pretty well, at which point they would think I'm so awesome for being so down-to-earth and not going around bragging about it. (I kind of blew it with you guys though, I'm sorry!

But I hope you understand I was trying to make a point here.)
Basically, I'm saying that the moment that they find out, afterwards, is a huge DHV for you, and the longer you wait, the bigger. And at the end of the day, you shouldn't need to play a card like fame or money in order to attract people you've just met.
By the way, if you don't mind me asking, would you be willing to say what sort of business you started? I'm just curious, as I'm saving up to start my own business as well.