When we apply for assignment of tasks, can we use "指示" instead of "指派" in Chinese?

When we apply for assignment of tasks, can we use “指示” instead of “指派” in Chinese?
指示 is usually from a higher level leader. 指派 is usually from a superior or project leader. 委托 is probably better.
This is some Chinese culture. Our team hopes to be softer. It would be great if you could help us.