Well, I would remove the fairing and get a nice round 7 inch headlight for it. That will change the look a lot on its own. You will need it off for some work anyways.
With the choke, you will need a new cable. So remove it but note its position. Now, where it connects to the carbs, try to move the part, if it moves then the choke in the carbs should be ok and it is just a stuck cable.
If the carbs themselves are stuck, it will be time to pull them off and clean them so you would drink through them, then clean them again. If you dip, make sure to remove every single rubber and plastic piece.
The minor oil leak would be hard to say. Is it just a weep where it slowly appears and is dirty? I have that on the left since of my bike, it is a low pressure side and is no big deal, BUT I have an sohc so this may not apply to you. It is just a thought and someone else might be able to back it up.
The rattle at low rpm, was the bike in motion or in neutral and just idling? If just neutral and idling, pull in the clutch ad see if it goes away. It is likely just a bit out of sync on the carbs, but it may be cam chain rattle so check those 2 things.
If you are keeping all that, there really isn't anything you can get rid of, so keep all the wiring. You COULD replace the connectors with new connectors, or cut them off and solder the wires. Those old connectors can raise a bunch of hell on a bike. Or get a new harness if you can find 1.
As for cutting anything up, wait till the fairing is off and you might have a whole different opinion of the bike.
The ride IS the adventure. The destination is just to get gas!