@Mervyn - The same options don't exist in the newer versions of Opera. In 12.16 you can edit existing search engines, delete any/all of them, as well as adding new ones.
In Opera 18 there are 5 preset search engines that can't be edited nor deleted - Google, Bing, Yahoo, Wikipedia and Amazon. However, you can make any of these search engines the default, and you can also add new search engines and make any of those the default, so maybe that's the solution.
Personally, I'm not a fan of the use of search engines in 18, simply because you can't edit/delete the 5 search engines that already exist in the program.