The question is fairly deep, but the answers may be a bit simpler than the question.
The legal entity is typically something like an incorporation. I don't know how Canada handles that exactly. That is best addressed by your lab.
As to the level and volume of the documentation, having a bit better idea of whether your lab is sizable or one-person or something in between, and what kind of material testing you do, would be helpful.
Generally, you must address every point in the Standard. Having stated that, some things may not apply. State that and why, and move on. Now, any clause that requires policy/procedure, and that does apply to your lab, must have the requirement actually addressed. In some cases, you may easily be able to include the policy/procedure in the quality manual. An example is document control, including computer systems, electronic document control, security and integrity of data, and confidentiality of information, all of which is SPECIFICALLY to be addressed.
Some parts are best handled with external procedures, referenced in the quality manual. An example is the procedure for measurement uncertainty, which is also a specific requirement. Procedures that are validated (e.g. ASTM) can be referenced.
Procedures developed by the lab must be validated, which requires a plan. the plan can be simple, and basically includes a description of the method, what it should do and not do, and what the acceptance results are. Have Management sign off on it. Then the report should include the results, related right back to the requirements outlined in the plan, and a specific statement as to whether the procedures is valid for intended use. The report is also to be signed off by Management.
You will also have to participate in at least one proficiency test or inter-laboratory comparison (PT/ILC). Check with SCC to see what they have available or can recommend.
All this sounds like a lot - and it is - but hopefully you'll pick up enough help to write the manual and succeed on your assessment.
Hope this helps.
Hershal