Final answer:
The nurse should delegate the task of assisting with ambulation to the assistive personnel, as it is appropriate for their skill set and critical for maintaining patient mobility.
Step-by-step explanation:
A nurse caring for a client with fluid volume overload has a range of tasks that need to be performed, some of which can be delegated to assistive personnel (AP). While administering medications such as diuretics and assessing lung sounds are within the scope of practice for a nurse, these tasks should not be delegated to an AP. Monitoring a patient's vital signs is sometimes performed by APs under the direct supervision of a registered nurse, focusing on accurate and sterile procedures. However, the most appropriate task to delegate in this scenario is assisting with ambulation. This is because it's essential to maintain patient mobility and prevent complications without requiring the clinical judgment reserved for nursing or advanced practice.