How do I trace the outline of a group of polygons?

Yes, boundary (object > shaping > boundary) is probably the answer here.

A possible exception is that if two objects do not exactly touch (but the gap is maybe only visible when you zoom in very tightly) boundary will create separate boundaries for the two objects. Also, note that the boundary is created around the object, ignoring outline thickness -- so with a conventional (centred) outline, cutting along the boundary line will leave only half the line thickness.

An answer to both of those problems is to convert the outlines to curves before applying the boundary. Then the boundary is created at the outer edge of the outline, which will often fill unnoticed gaps between objects -- ensuring a single boundary for objects that are almost-touching as well as those which overlap. But note then that there is no tolerance between the boundary and the object's outline. So, it is probably desirable to duplicate the boundary and apply a printing outline to that, ensuring a bit of tolerance between the cut line and the printed image.

And finally, it is often wanted to have a white border around a cut shape. You can achieve that by grouping the objects and making an outside contour from them.