It ends up costing a little more in the long run, but you also get a better quality product.
Working with a good ux designer will completely change your understanding of the role of design in product development. They can play a pivotal role in defining and shaping your product. And yes, a person with these qualities almost invariably can also code. Understanding the underpinning technologies of the web remains nearly inextricably entwined with understanding the design potential of the web.
As an aside, I think a platonic ideal founding team would have 2-3 people who share varying degrees of business, design and technical acumen. Each person has a defined role, but they also relate to their co-founders' roles in a meaningful way. Really understanding what it means to be GREAT at something often requires educating yourself enough to become mediocre at it. Completely partitioned specialization is for companies big enough to need HR departments.
Umm...why not? You just said you'd never hand your stuff over to them, so what basis do you have for not trusting them?
I've personally had great results with several of them, much better than I've had with many designers.
Web designers that can't code are just designers. So make sure you hire a web designer for your website and you will get a better result.
Also, the majority of professional webdesigner out there are starting prototype with CSS.
I'm a programmer by night / business type by day. I have a website soon to be released in beta and I hired a designer I trusted (and could afford) from a previous job. She worked wonders for the project -- seeing the new design also reinvigorated me.
A few tips: Hire a friend if possible (you'll probably get a friend-rate), if not work by referral. You want someone you can sit with face to face. Avoid 99Designs and the like if you can. Pay your invoices immediately and you'll find the designer will likely continue to be super helpful. Also, get an hourly rate up front since you'll probably find things that need to be adjusted. Lastly, I wouldn't use the designer for HTML, just have them hand off PSDs, the markup tends to be not so good. Insist on PSDs, not flattened images.
By the way, I'm happy to give a refferal for a trusted friend. Just email me at juliuss at gmail.