Welcome to the forums :) Without seeing the file it's always harder to give accurate advice, but a good starting point is: Select All (Cmd+A), go to the Stroke Panel (at the top right of the default workspace) and click the solid line style, then click in the text edit box and type 0.01mm and press enter. Now go to the Colour panel (again at the top right of the default workspace). Select the fill colour context from the control at the top left of the Colour panel (i.e. choose the filled circle at the bottom right of that control) and select the special 'None' fill from the bottom left of that colour context control. Now choose the line colour context (by clicking the outline circle at the top left of that colour context control). Just above the very top right of the colour panel is a little menu dropdown button - click it and choose 'Sliders' and now choose 'RGB' from the list of available colour formats. Either slide the sliders or type in the 0, 0, 255 value you require.
If you have any text in your file then you can get the most predictable results by simply selecting it and clicking 'Convert To Curves' so that it doesn't matter if the person doing the work for you doesn't have your font or their application displays it differently - it will simply be the curves you see, rather than editable text now.
Hopefully if you now go to File->Export and choose either SVG or EPS you should have a working file, just as you expect. It might be a very good idea to confirm with the person doing the cutting that the file meets their needs, but it sounds like it should.
devonl got a reaction from Dale in Export outline only with specific stroke/colour