If you are going cabinet hunting, a quick way of telling if a cabinet is a Kenmore cabinet is the opening will have sharp corners. Singer and others will have rounded corners. This can save you a little time when searching on CL and Ebay if you are looking for a cabinet for a Singer machine. You will still have to measure the hinge pin distance on the cabinets with rounded corners in the openings.
Another thing you can try if you don't want a cabinet is to post a wanted ad on CL for a vintage Singer sewing machine case or base. I was looking for the same thing you are - a base for a 15-91. I got an original Singer grass cloth case for 5.00. It can never hurt to ask. I wouldn't pay more than 20.00 for a full case if you can avoid it.