A. Weighing the child: This can be done safely without causing airway obstruction, though it is not the priority in respiratory distress. B. Assessing the child's vital signs: Necessary to monitor the child's condition and does not exacerbate epiglottitis. C. Inspecting the child's mouth and throat with a tongue blade: This is contraindicated as it can cause airway spasm and complete obstruction in a child with epiglottitis. D. Listening to the child's lungs: Safe and part of the assessment for respiratory distress.