there is no such thing as 'can't be done' Things get done...can't say if there would be no marks left after you're done. You can douse the pin in WD40 or whatever for a month but it would still act-up. There are ridges formed on the pin where each segment of the hinge rotates, add to it the rust which has bonded the two surfaces and you have a problem that can be best described as 'Laaton key bhoot baaton sey nahi mantey"
I suggest you remove the door from the hinges by removing the screws and doing whatever it is that you wish to do afterwords. Leave the pin removal to the experts. Having said that, the removal of screws may not be an easy task itself. The same rust plays havoc in this area too.
I would get a long stem screwdriver that has a thick enuff head to properly fit the screw head then slip a 10 mm spanner on the stem. It works best if you have another person to help you. One person can push against the screw while the other turns the screwdriver with the help of the spanner. Lemme know if you want me to explain further
I wish you luck my friend.