They look really similar, but under the hood, they're really quite different. I just pulled my book out to see how different, because I'm curious.
In a quick look, they can share a few bolts, the stitch length plate (but not the mechanism and lever behind it), the side arm plate, needle plate, balance wheel, and a few things like that. Even the take up lever is different, and the needle bar for sure (based on part number)
The part number for the hook you're looking for quilt'nmomma is 45271, and when I looked it up on sewing parts online, it said these are the machines that use the same hook:
201-2, 1200, 1200-1, 935U
I find it curious that all of the charts I have only refer to the 201-2 (potted motor), not the 201-1 or the 201-3. I hope if yours is one of the other ones that the hook number is the same. If I can check mine (201-3) while I'm giving it's "welcome to your new home" cleaning / tuneup, I'll post back and let you know for sure.
So please don't take your 66 apart, it won't help either machine!