Ok, so it's not so much a trick as it is an appliance. To remove bandaids without sticking to little hairs, or additional scabs or wounds that lie underneath, all you need is a blow dryer. Simply turn it on low and warm the band-aid.
When the adhesive has had time to melt, the band-aid will pull right off - without any screaming, wincing, flinching or whatever horrible noises kids make in preparation for band-aid removal. See — told you it was simple and it will save you a load of headache!