Reinforcing delicate 1941 speaker cones.

I would only like to point out that anything you do to the cone will most likely degrade the value of the driver. 

No

You might research this, though it most/ALL likely will alter the sound somewhat (see link).

Do you have backlight showing through folds/ridges on the cone (I'm experiencing this on my favorite pair of vintage paper cone drivers and I will probably try a light "directed" application of Puzzle Coat)?

Please describe the weakness you perceive.

https://www.t-linespeakers.org/design/tweeks.html

DeKay

Be careful what you ask for.  Not only would changing/adding anything to those drivers diminish their value, you’ll also change the sound qualities of them.