If you want thinner than normal Cat6 but can handle a bit more than 0.9mm, there is also thin Cat6 available: https://www.monoprice.com/product?p_id=34213 https

If you want thinner than normal Cat6 but can handle a bit more than 0.9mm, there is also thin Cat6 available: https://www.monoprice.com/product?p_id=34213 https://www.monoprice.com/product?p_id=34213 It's 2.6mm diameter, and I had success running it between baseboards and carpet.