Thank you for the question. There will always be some scarring with either method of removal (shave removal and surgical excision). The anatomic location of the mole, the pigmentation of the mole, and if it is raised or flat will all dictate which method should yield the least amount of scarring. Cauterizing a wound often leaves more scarring with shave removal as compared to other methods that stop any bleeding (e.g. styptic medication or direct pressure). I would recommend seeing a board-certified dermatologist who has an interest in cosmetic dermatology to discuss your treatment options.
Thank you for your question. Any type of injury to the skin will cause a scar, so there is no type of closure that prevents a scar. With that being said, your question of to close with stitches or no stitches depends on the type of scar you want. A shave excision, similar to what your wife had done, will generally leave a circular atrophic scar; whereas, an excision with stitches will leave a line as a scar. The type of procedure and closure depends on the size and location of the lesions to be removed. I highly recommend you consult with a board certified dermatologist or plastic surgeon to have your lesions evaluated and to discuss treatment options that best suits your needs. Take care and good luck.