When I hire a contractor (plumber, carpenter, window washer, appliance installer), they are required to show that they have worker's compensation insurance (if I ask). Worker's Compensation only covers employees of business entities. Frankly, I do not think that if I was injured doing a mystery shop the NJ Division of Labor would try to force the MSC to cover me. First, they would ask me for proof of employment including my starting date, hours I worked, paychecks, etc. I would have none of those. A contractor is not an employee. California has been trying unsuccessfully to classify Uber and Lyft drivers (and others) as employees, and as far as I can tell, they have not succeeded.
I have an LLC that I use for consulting. Some large companies have required that I provide proof of general liability insurance, workers' compensation, etc. when they contract for my services. There are some specialized insurance companies that provide very short-term policies at low cost (since the probability of a claim during a 1 or 2-day period is low). I often opt to be an employee of an agency that serves as my broker. They get a cut of my compensation, but they worry about insurance, etc., and can FAX all of the required proof to the company that is using my services.
Shopping Southeast Pennsylvania, Delaware above the canal, and South Jersey since 2008