Dear Redbopeep,
Benz is right, you will just have to suck it and see!
This is why professional rigging lofts have an advantage. They all made thier mistakes years ago and have the right materials laying around to hand so it is easy to make up a test peice to make sure everthing fits.
For 3/8 wire I would use 2.5 or 3 mm diameter black plaited polyester cord. ( V.B. or venetian blind cord we call it in Australia.) I would not worry about the parcelling thickness, just use athletic strapping tape, White Linen, non-elastic, commonly called Leuko tape around here. This is pretty thin and will squeeze down fairly well.
Best of luck.
Joe Henderson.
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