Final answer:
Using a vibrating device to stimulate the skin is a proper nursing intervention for cutaneous stimulation to relieve pain in pediatric clients.
Step-by-step explanation:
To relieve pain with pediatric clients, the nursing intervention that demonstrates proper use of cutaneous stimulation is using a vibrating device to stimulate the skin around the painful area. Cutaneous stimulation, such as vibration, can help distract from pain and promote comfort. Applying a cold compress or massaging with warm oil may have other benefits, but they do not directly target cutaneous stimulation for pain relief.