Once you find a restorer Westoe, it might be of interest to many of us to see a "before" and "after" photo, and if you don't mind, an estimate of cost to undertake the restoration, in case others find themselves in a similar situation.
I am sure that each restoration will entail different challenges so no case will be the same, but a guide might be useful.
My sister had a couple of oil paintings (on board, not canvas) restored several years ago. The restorer required cash up front in order to purchase the materials (which I thought seemed odd). I think he may have needed to match paint colours and I believe he used something which softened the dried and flaked paint. I think it cost in the many hundreds of (Australian) dollars, but the restorer did a good job.
Good luck with your restoration.
Added: I believe that the usefulness of the laser may depend on how the work was painted. If the artist drew outlines and then infilled with paint, you may find the laser picks up on overpainted linework. However this still may not be accurate as an artist may draw then redraw linework and when painting over this, may vary it again. You have not given much detail about the work or the damage, but if the mouth was damaged I'm afraid you might have to be content with a restorer's impression of how the original looked.
