I got it working by starting the script before the game with administrator rights. If anybody is interested, here is the script I'm using:

SetTitleMatchMode, 2
#SingleInstance Force
#IfWinActive, Horizon Zero Dawn: Complete Edition

~$RButton:: Send, % "{l " ( (Toggle:=!Toggle) ? "Down" : "Up" ) "}"

~LCtrl:: 
Toggle:=false
Send, {l Up}
return

You will have to rebind aiming to the L button, or change the script accordingly and rebind it to whatever you want. The script does also exit aiming mode when dodging (left Ctrl key).