I will try to give a very high level review, since you did not ask a lot of questions in your question. Keep in mind that there are many ways to solve this problem, and I will try to give one solution, which, it seems to me, is easy to understand.
This post assumes that if your site is www.company.com , you should download static content from www.companycdn.com . And this new site ( www.companycdn.com ) is a simple static website that does not support cookies.
To do this, you need to upload your static resource (for example, images) to the second domain.
And then update the image paths to the new domain. For example, instead: <img src="logo.jpg"/> , you should change it to <img src="//www.companycdn.com/logo.jpg"/>
This answer contains additional information: https://webmasters.stackexchange.com/questions/1772/how-do-i-set-up-a-cookie-less-domain
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