What does your topology look like? If the holes on the mesh are bordered by clean topology or polygroups, you can use the Stroke > Curve Functions > Frame Mesh function to create a curve based on either the border of a mesh opening, the border of a polygroup, or a creased edge.
If you can’t figure out an approach using that to get the curve you want, you can always manually draw and edit them with the Topology Brush.
Once you have the curve you want, if you enable Curve Mode for a selected Brush, you can apply the stroke all at once to the curve by clicking on it. If you have trouble getting the stroke to draw out without deforming the curve, try lightly contacting the curve with the brush, then pressing Shift.