Your OM provides a quote from ICAO Doc 8168 and is correct, however there is a paragraph before that says:
1.1 Nothing in these procedures shall prevent the pilot-in-command from exercising authority for the safe
operation of the aeroplane.
So, there is nothing stopping you from operating the aircraft in a different manner, if you deem it is safer.
If you're an EASA operator, then all departures anywhere in the world are required to be Noise Abatement departures - see CAT.OP.MPA.130 and associated AMC. So there is no discretion not to!
AMC is not legally binding, it merely provides a way to implement legislation in the Operations Manual. There is nothing (bar an authority with lack of any common sense) stopping you from implementing something different than what AMC says.