So 3.7 mm cable should work fine?

Yes, it can cover a range of diameters, it just won't cover as far if it's on the thicker side.

What material is this?

it feels like telephone cord, but on smaller scale.

is this gonna work with 1/8 in dia headset cable?

I believe so, but I use these for my iPhone chargers which is 2mm. It is a tight fit, so I imagine it would, but have only used on 2mm or larger cables. Not as sure about smaller ones

ASIN	B08PZ5P998
Best Sellers Rank	#7,656 in Electronics ( See Top 100 in Electronics ) #51 in Cable Sleeves
Customer Reviews	4.3 4.3 out of 5 stars (682)
Date First Available	December 8, 2020
Item Weight	0.634 ounces
Manufacturer	YeHeng
Product Dimensions	60 x 2 x 0.04 inches

Cable Protector Animal Proof Wire Repair, Cord Protector for Pets Headphone Saver Spiral Cable Wrap Strain Relief, Cord Sleeve for Phone Cable USB Date Cable, 60 inches, 2 pcs, Black

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