First what you need to control is anchor texts. If the tool you use uses one commercial keyword as anchor text for all sites it is a big problem for your link profile potentially.  For a start check your backlink profile and see the anchors (use MajesticSEO or Ahrefs for this). For natural profile most used anchors will be brand names, url as anchor or domain name as anchor.

For your case I recommend two possible solutions. The first one: write unique descriptions of your products. The second one: set up canonical urls from one domain on another, for example from uk domain to us domain. It will be the sign for Google that content on uk domain is duplicate and original on us domain. Of course your uk domain will not rank well, but you will avoid duplicated content problems. As you see much better solution will be just write unique content. And it will give you more freedom for domain targeting and will be much more smarter solution.

You can build your site on clear HTML but it solution is from past century and it very unproductive way. If question is about choice of CMS - big count of  CMS  is SEO friendly, you not must select Wordpress only.