I used hand cleaner (GoJo type hand cleaner) on my Singer machines that were painted. It works very well. It gets rid of all that stuff that appears to be nicotine. I used Brasso on the chrome. I pretty much followed the videos listed below. Your machine is painted, not shellac'd like the one she is cleaning. Do not use WD-40. If you need a solvent, use Gun Scrubber.
Good rescue!
How to clean an oil a vintage sewing machine
http://www.youtube.com/watch?v=bidpJ..._order&list=UL
Don't go away, relax, pour some more tea, and stay tuned for part 2!
http://www.youtube.com/watch?v=SKR5t..._order&list=UL
bk