user research – formative usability tests – Script

I'm running my first real usability test.
I'm doing this for an internal business application that will eventually be offered as a SasS.

I recruited a small group of users that literally represents 100% of our national users. (It will be an international product for a very specialized industry).

I have done a task analysis and I have had multiple opportunities for contextual observation.

I analyzed your current system, interviewed current users and reviewed the analytical and business data to better understand the needs of users and businesses.

I have created a semi-interactive medium fidelity prototype to run an initial and formative usability test.

My question is: how important is the script?

I have created a small task script.
That is to say)

1) Log in, search for the "X" client by name.

2) Identify the customer's mailing address.

3) Find navigation instructions to the client's address.

Although these tasks are based on a real representation of the daily tasks performed by a user, I understand that a usability test follows much more than a scripted version.

Is there anything wrong with making a task-based script if it is a true representation of the users' daily workflow?

Do I really need to say things like "you are working for XXXX, a customer's phone, do you need to locate this customer in the system"? Or I can simply give the user very small and specific tasks.

I ask because this, being my first time, makes me uncomfortable. I prefer to give them simple tasks and analysis. But at the same time, if this distorts my results, I'll take the time to write a script.

What you think? What has been your experience?