What are the best ways to find an external thesis examiner?
Start by going through the bibliography of your thesis draft.  For each author, consider whether they might reasonably be an external examiner (e.g. are they established scholars with a reasonable reputation, do they hold positions as professors in your discipline, etc.)  This should produce a large list of potential external examiners. 

I'd encourage you to get your advisor to contact prospective external examiners rather than contacting them yourself.