The main benefit of putting a Stax cable on a pair of ESP-950's is not to change the sound, but to allow driving them with a Stax amp. There is a dongle-adapter available to allow use of phones with Stax 5-pin 'PRO' plugs from the Koss amplifier. So, with a Stax cable on a set of ESP-950's you could use the Koss on a Stax amp, and with the dongle, use them also on the Koss amp.
I'll leave it up to others to decide if wire changes the sound in some appreciable way. ( Although I must say I once posted a $400 wager open to anyone who could hear the difference in a double-blind level-matched comparison between one meter of 24 ga stranded copper wire and an equivalent length of silver wire in at least 6 out of 10 comparisons. None of the guys who were posting about how they "absolutely could hear the difference between copper and silver" were willing to put their money where their mouth was. )