Purpose of metal sheath in display cable?
The signals going to the display are quite high frequency.

That conductive shield shields the radio-frequency emissions of those signal wires, this prevents these emissions from the product violating EMI emission rulings but also it helps to prevent other sensitive circuits in the product (for example a microphone or WiFi receiver) from being disturbed.

It is very well possible that everything will work as expected even without the shield, however there are no guarantees. The sane/easy choice is to simply keep some form of shield in place to prevent issues.