Looking at my 1949 Remington-Rand Model 7, the spring is not in the pivot point of the carriage lever, but under a boomerang shaped lever which pulls the line spacing dog. The lever is immediately below the carriage lever and interfaces with the carriage lever through a barrel shaped bushing that rotates on a post. The pivot point of this boomerang shaped lever under the carriage lever is where the spring sits.
A brief look shows the spring is just under a millimeter, so probably about 20 ga wire. Mine has 2 completed loops and part of a third, wound counterclockwise. Looking from the top, with the spring in a wide V shape, the lower end is the left side and upper is the right side. Left side pushes against a stop on the carriage frame. Right side pushes against a catch on the underside of the boomerang shaped lever. Left terminus should be 1/2" from the center pivot and right should be 5/8" from the center pivot point.
This is a really strong spring, so you might start with a wire that only has maybe 2 loops, with both terminating ends parallel, needing installation to fully complete tension. I really wouldn't want to pull this spring off, considering how small it is and how fast it would want to hit one wall, ricochet then bury itself across the room under your baseboard or your [fill in the blank]. Then you'll be making all the noise that your noiseless didn't.
I hope this helped.
Good luck!
Phil Forrest

If you have a bicycle shop with a mechanic who has been in the business since the 90s or earlier, you should be able to find the spring you need there. This is also the kind of spring you'll find in some smaller pruning shears.
One thing I forgot to mention in my previous post:  the diameter of the coils in the tensioned spring looks to be about 1/4".

Phil Forrest