How to bring on someone to take over?

I have a web dev company, and farm virtually all work out to some really good programmers overseas. Things are going well - we have no debt, a good amount saved up (could live off it for 3 years assuming no major calamaties came up, which of course, they would), and residual from hosting that (for now) takes care of much of our monthly needs.

Yet, the problem persists: If business is slow, I FLIP OUT. I worry about way too much. I worry about going backwards, slowing down, etc. I think the only way I can lower the anxiety is to step away from the biz a bit. I just don’t know how. This business is my baby, and has been for about a decade. I don’t want to just hand it over to someone. I do know I need people that are super trustworthy to handle clients, and others that are fired up to get more biz.

What are your suggestions?

What are your day-to-day roles with the company? I assume that, as all work is farmed out to programmers that you’re either a designer or out there trying to rustle up sales?

what I do basically is I just sit here, responding to emails and answer the phone, or perhaps get my hands a bit dirty in code / design.

That is a life balance problem. Look at what you do with yourself outside of the business.