I mean is there (hopefully good) flexible 4 core braided cable or only 8 and 16 core braided ones?
Here's some 4 strand braided silver plated wire for a decent price: https://www.ebay.com/itm/4-Core-Bra...DIY-Amplifier-Headphone-Earphone/272993698275
Talking from experience it's very soft and perfect for earbuds. (look at my profile pic, same wire)