What you are doing is a simple exercise to eliminate waste, although explained through a lofty term "process improvement of skill matrix using value stream mapping."
Research Objective
Questionnaires are a method to discover unexpected relationships or to confirm something you have a hunch about. Now, you have to ask yourself, what is your research objective here? What are you trying to find? If you are able to frame it, then work backward and design your questionnaire.
Remember, you can torture data to say what you want to hear. But that's where research gets a bad name.
Process Flow Map
Ideally, you should have a process flow map of the existing process, which identifies the tasks, wait times, delays, and the length of the tasks. If you have that on paper, it's easier for you to focus on the problem areas such as delays, wait times, and the length of tasks. You can then go ahead and try to address these issues. Now, when you are trying to address these issues, there might be a potential case for engaging a questionnaire. A word of caution - don't try to have one just for the sake of having one.
Once you have addressed the problem areas, you may want to come up with a revised process flow map to compare the efficiencies.
Your research could be more dependent on empirical evidence, which is an alternative research method to using questionnaires.
Hope this helps.
Cheers,
Saj