Those bikes look great . Nice site.
To have a separate webshop is very common. You often see sites that link to "the shop".
So set up a new page called Shop from your main site, and on that page you configure all the menus and modules for your shop. Just use Joomlas features as to what appears and does not - that's so easy. You suggest you want an entirely new template for your shop but keep it under your main domain name. Joomla is great! Hikashop is too!
For the styling, you need to ask the Hikashop guys whether you can take their style. I have no idea if they developed a template from the ground up, or bought a template. It would be very wrong to simply take the style without understanding the copyright. I'm not a fan of templates; I like artisteer where you can create something unique, but that has limitations too and needs post work.
If you really like the demo site, send Nicholas a PM and see what he says. Presentation is very different from content.
Tony