What a cool old razor! If it were me, this is what I'd do, purchase some crocus cloth, standard and fine auto paint rubbing compounds. You'll need some alcohol or mineral spirits to get that tape gum off so you may as well go ahead and clean the scales too. Caution! Alcohol can destroy your scales so only use it as a contact cleaner and get it off of them. As for the blade you can soak it in alcohol to disinfect it, then hot soapy water with a tooth brush. Next tear off some small strips of crocus cloth and dip into that coarse rubbing compound to clean the blade. Be careful how much pressure you put on it not to crack or break the thin edge or scales. You would do well to rest it on a piece of card board laid on a board. That way you will have a dampening affect and not scratch any progress you make. Rub it well to get all the rust and most of the heaviest patina off. Then use a piece of either the back of the crocus cloth or some cheese cloth to polish it with the fine rubbing compound. This will not get you to a mirror finish. This method is only intended to clean up your razor so you'll have a clean old razor with lots of character and not wash out your blade etching. Next, you'll need to hone it and strop it before use. I don't know what your experience level for that is.

Good luck.

Show us your progress.

Regards

Chasmo