I'm in the restaurant industry myself, and the best piece of advise I could give you is not to pigeon hole yourself... niche markets are great, but given the lifespan of a restaurant and the risk involved means that you have to try and appeal to as broad a customer base as you can, and by branding yourself as a SW restaurant you would seriously limit your overall appeal.
As a couple of people have said, I don't think SW approval is necessarily the way to go, as I can imagine that the fees / audits involved would make the whole thing prohibitive, however healthy eating is on the rise and being able to cater to everyone with delicious and healthy meals is an excellent idea. I would approach this as a healthy / fresh / natural concept, focusing on the fact that everything is prepared from scratch using (if possible) local produce and catering to those looking for good food that remains health conscious. I think the reason a cafe is more likely to develop in this direction is that when people go out for a meal in a restaurant, there is the feeling of 'treating' yourself and the minute they think it's a diet restaurant it will, unfortunately act as a turn off because they don't realize that you can eat healthily and well at the same time
I completely understand the fact that you would want to go the restaurant route, and maybe a bistro style restaurant would be the way to go, open for lunch a dinner, with a menu that can be adapted to all the core diets / ways of eating out there... SW / calorie counting / low carb and so on... it would take quite a bit of research, but when I think about what I cook it's actually easy to adapt, you could then work out a personalized value / rating system that would tell customers what each dish contains.
Anyway, I've waffled on for way too long

I think it's a great idea and well worth exploring! Good luck
Kay x