The sound does not occur when using any mouse selected menus. Only when a keyboard combo is pressed.
This strongly suggests it's tied to the cmd-key, not the Copy or Paste action.
The sound is whatever I choose it to be in the sound panel in system preferences. ...
This means it's almost certainly being triggered by the NSBeep function that plays an alert sound.
The issue does not occur in safe mode and in my guest account it makes the standard error sound but the issue I'm having does not occur.
This means it's happening because there's a per-user setting or preference that's causing something which leads to an NSBeep.
All my accessibility settings are set to OS X default (quickly checked that now in case it had something to do with it).
Did you check System Preferences > Keyboard > Keyboard Shortcuts?
I suggest a two-step process:
1. Go through every pane and setting under Keyboard Shortcuts, and write down the state of everything.
2. Click the "Restore Defaults" button.
I don't know if "Restore Defaults" applies to just the current subpane, as selected in the left-hand list, or whether it means all shortcuts in all subpanes will be restored to the defaults. If you don't care, then feel free to ignore step 1.
After clicking "Restore Defaults", do a cmd-C test in TextEdit. Is the problem solved or not?
If solved, then the likely culprit is that some Service or Shortcut was assigned to cmd-C and/or cmd-V, but that Service or Shortcut was actually unable to run, and that failure to run lead to the NSBeep.
If the problem is solved, go through your written-down list and set the shortcuts to the correct on/off state and keystroke. Manually test cmd-C in TextEdit after each one, to confirm it still works.
If the problem isn't solved, go through every subpane of Keyboard Shortcuts and manually uncheck every item in every subpane. Is the problem solved then?
After checking all of this I can only assume that it is a software change that is influencing it. However I have been running the same setup for the last 6 months. The ONLY new software aside from updates that has been installed in that time is Spotify and Google Chrome (which I only use for US Netflix). Both of those apps I have removed using CleanMyMac to ensure there are no remnants, followed by automated scripts via Onyx. Didn't fix the issue.
CleanMyMac is not considered harmless:
https://forums.macrumors.com/posts/18271411/
The only thing I haven't tried yet is a different keyboard (I don't have one). It's an unlikely culprit but I'd like to rule it out.
I think it's very unlikely to be related to the attached keyboard.
... What I'd like to know is where those systems sound live. I'd just use Audacity to blank the sound out and save over it. At least then I could pick a "silent" sound effect from the list.
See here:
https://forums.macrumors.com/threads/1062929/
Resist any and all temptation to modify /System/Library/Sounds directly, because any changes may be overwritten the next time an OS update is applied.
Instead put your custom sound in either your per-user ~/Library/Sounds folder, or system-wide in /Library/Sounds.