Dolly .. just my opinion and bear in mind I am not an antique expert by any stretch of the imagination ...
... The only items (machine or cabinet) I would not dare to refinish are pieces that are very rare (meaning less than 100 survived) or have historical significance (ie documented provenance that it belonged to Mary Todd). A mass produced Singer cabinet is neither. If the item is going to live in my house and be displayed in my house, I want it to look pretty. Almost all of my cabinets are going to undergo a degree of restoration/refinishing (stripping varnish on wood, replacing veneers, sand blasting irons and re-painting, re-plating metals, replacing screws, re-upholstering stool bench seat).
So if the discoloration bothers you and this is not a rare cabinet ... go ahead and refinish it.