Two things to consider before you do this:
1. While changing to .com may make your business seem more global, it will also undermine the fact that you're a UK business. While your overseas sales may increase, your UK sales may also decrease as a result.
2. If overseas visitors are actually making it to your site, then they've overcome the hurdle of your domain name. Surely a better approach would be to state more clearly on the site that you ship overseas and that your shipping fees are competitive.
It's probable that you're just getting less activity from overseas traffic just because of your physical location. If so, neither a domain change or an on-page copy change is going to have much of an impact.
Also consider that if you are not hosted in the UK, switching from a .co.uk to a .com will drop you out of Google's regional SERPs.
If after all of that you still want to go ahead then set up the .com as your main domain, and set up requests to .co.uk pages to do a 301 permanent redirect to their .com equivalents.