Early car, Wurth waterborne is my experience
The 67 S that I have (45,000 miles) has undercoating similar if not exactly the same as used on the 356. It is original & unmolested in the trunk, u pristine. I understand the original product contained asbestos and you could purchase it up until the early 90's and believe it was called Body Schutz. The early product did show some particles that were not black and looked like asbestos particles, and could look grey after many years.
The petroleum base product ends up thin no matter what pressure, what temperature. Unsatisfactory in my opinion. And a fire and breathing hazard for sure. The water base dries very hard but is temperature sensitive. It is best used when the product dries quickly with a warm temperature (above 80 degrees F if possible), more texture, more close to original and the only product other than a shop made product that works. You should experiment with pressure, distance and coverage just like paint so you know what you will get when you spray the car. Both give off fumes so you should use with ventilation. And don't get it on any surface you don't want it on. Particularly a painted body. If it dries you have a problem.
If it were me, I would paint the bottom of the car with your choice of rust preventive paint if you have bare metal. Then undercoat. I just received 5 cases so they do ship in winter but the product is freeze sensitive.
As everyone that has restored a later car with the heavy undercoating, that is a horse of a different color. Very difficult to remove, it can be closely duplicated but does take some practice and product/equipment not readily available. Lots of work.