Did you contact either Midget or JR trailers to purchase cable? They will know the right diameter at least. I'm pretty sure there's nothing special about these cables...i.e. they're not stainless steel.
A cheapie digital caliper would give you a definitive answer on diameter, though I think your measuring tape would be sufficient.
https://www.amazon.com/Tacklife-DC01...rds=micrometer
Here's a write-up on replacing and adjusting the cables:
http://www.hilotrailerforum.com/f22/...djustment-125/
It looks very thorough, at 15 pages in length.
Harbor Freight sells a 50' roll of 5/32" wire rope for $10.
https://www.harborfreight.com/50-ft-...ope-69799.html
Or 100' for less than $15.
Does this help?
Good luck
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