Based on the information provided, I'm afraid the answer is 'no'.
These are the only ways I know to get an outline for cutting:
-- Path menu > Union (boolean)
-- use Pen/Bezier tool and trace
-- import PNG and use Trace Bitmap
If we could see your file, we might be able to suggest some shortcuts. For example, what if you select only the parts of the drawing which make up the outline, and move them either to another layer, or another file. Then maybe Union would not take so much time? Or there might be other ways. But it's impossible to guess -- we need to see the SVG file.