If you only want them to search by All Words, set the default and disable the search mode for the web part.
If you want to change the order in the dropdown, you will have to clone the web part and the module. The values in the drop down are added from an Enum. You might be able to set sort to true for it.
ControlsHelper.FillListControlWithEnum<SearchModeEnum>(drpSearchMode, "srch.dialog", useStringRepresentation: true, true);
A more hacky way would be to modify the order of the drop down with JS after the page loads. Probably wouldn't recommend this method.
You could also not use that webpart, and just use custom html/js. Just add a textbox, dropdown with the items in the order you want, and a button. When the button is clicked just redirect to the results page with the querystring parameters set: "?searchtext=test&searchmode=anyword"