Sit down to wash. This saves energy for other things later on.
If washing at a sink or basin make sure all the items they need are close by. This saves time and effort of getting up and down several times.
A hand sized sponge is lighter and easier to squeeze out than a towelling face cloth.
An electric shaver is easier than a wet shave with a razor. Some electric shavers have a built in balm dispenser and can be used wet or dry.
Pacing the task is more effective. If the task is difficult, the person may be tempted to rush to try and get it over with quickly. However they are more likely to be breathless, tense, and less likely to thoroughly wash and dry themselves.
Try to wash in a well ventilated room which has a comfortable temperature. If the room is too cold this can make the person rush the task and cold air could make them cough more.
Ensure the person has good mouth care and brushes the teeth or dentures regularly. If they use a steroid inhaler always rinse the mouth and gargle with water after use, this helps to prevent oral thrush.