The cable won't increase or decrease input delay as you found. The delay happens with the processing of the monitor. Using an HDMI 1.x cable will only really start causing you problems when you want to render 4K resolutions or higher at higher than 30hz. How much did you pay for the monitor if you don't mind me asking?
Ironically enough I don't think this has any effect on the lag... HDMI 2.0 Cables only have better Bandwidth... I'm pretty sure the lag is still the same.
Still though... you never know when you might need more Bandwidth.