Both types of cards are the same physical size (42.8 mm x 36.4 mm x 3.3 mm) but the guide rails are different. Looking at the picture below, you can see that the CF card reader has two rails to guide the card and each of those rails are "male" so the minimum distance between the rails in the reader is something less than 36.4. Let's just say the height of the rail in the reader is 2 mm, then the space between the rails would be 32.4 mm (36.4 - 4). But examining the CFast card, it is 36.4 mm total width, one side being "male" and the other being flat.
I think I would evaluate which is the least expensive of the two devices and then plan on destroying that device. That would would likely make the reader expendable. That of course is dependent on the cost of the two devices and is even more supported if there are desirable images on the card. Having said that, perhaps spray some WD-40 into the area of both sides and grab the card with some pliers and pull. Perhaps protect the card and improve the grip with a rubber band. WD-40 won’t likely damage the card, it may damage the reader, but perhaps only temporarily as it could be cleaned with alcohol.
Lastly, post the exact make and model of the card reader. Perhaps there is some content on the web about disassembling the reader.

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