I'm not sure of the dimensions on the 99 or which cabinet you are referring to, so can't give you a definitive answer for that.
Macybaby is an expert in accessories. She will probably chime in. You can also look them up by the number on them. Just search for Singer xxxxxx (insert part number for x's). That will tell you what you want to know.
What you need is the cradle. It will fit in all the later Singer cabinets. I'm not sure if the cradle will fit in the earlier cabinets.
bkay