15 volt zener and 1k resister is for reduce and stabilized the voltage for op amp. TL072 tolerate maximum 36V so u can omit them. but in real designer rule it will help the circuit operation stability. when you turn your volume high total dc supply voltage become unstable and op amp will produce noise if you omit the zener and 1k resister. you do at least insert 1.5k resister in place of 1k resister and omit only zener diode.I don't know why u hate zener. in this design 15 volt zener produce no any junction break down noise in the amp power line, u can use 18v , 20v , 24v zener also. or use 7815 or 7818 voltage regulator for op amp. i was use 15 volt zener.