I have a suggestion to make it even more powerful. Turn the mockups into a blog. This will benefit you in a few ways
1) You'll be able to grow your audience as a designer / consultant
2) It will provide you endless ways to pump out content to the audience you're building, allowing you to position yourself as an expert in your field and rank in search engines for terms related to UX design and design improvement.
3) You can do write ups on the blog which will be valuable to your following as you grow it and you'll start to get a reputation and more people will begin to approach you asking to design for them.
The above is a great long term way to demonstrate your skills and gather a network of peers in your field.
You could simply email the company the page of your website,
"Hello hope you don't mind,
I've taken a look at your website and I've used it as a case study for how I would improve it in order to benefit your conversion rates (whatever you guess their goals might be). I hope you like the publicity, perhaps you'd like to work together to make this happen?"
The above seems like a more credible way to go about this, you're giving them value for free, you're giving free and valuable information to an audience which demonstrates you care about the field and are keeping on the top of your game to your potential prospects. And you've got a handful of other example case studies that these prospects can look at demonstrating your ability to redesign things for businesses. Showing that you are the real deal and you have lots of good ideas. They will want a piece of your pie, most likely.
Instead, look for companies that do seem to get it. Build a short list of design savvy firms. Then reach out to the chief decision makers CTO/VP/Director.