How can I edit the original Myst app so that it no longer requires the CD to play?
You could make a disk image of the Myst CD and mount that for sheepshaver.

The original Myst for Mac was indeed an enormous Hypercard script. The Myst: prefixes you refer to are the program referencing the Myst CD. Classic Mac OS used colons as directory delimiters, so the file paths would appear as Myst:Images:Clocktower.jpg in Classic Mac OS or /Volumes/Myst/Images/Clocktower.jpg in OS X. You'll need to rewrite the paths to point to some local file directory. 

Say you installed the Myst app in an Applications folder at the root of the system disk. (This is the OS X location and is not correct or typical for Classic Mac OS, but I have no idea where Classic users stuck apps, so I'll use OS X conventions as a fallback.) This would be /Applications in OS X, so it's Macintosh HD:Applications in Classic (assuming, of course, that you haven't renamed the boot disk). Drag the contents of the Myst CD to a Myst folder on the root level of the boot disk (Macintosh HD:Myst:). Then you can re-point all the file paths in Myst to that directory.

Programming note: I'm on Windows at work at the moment, so I've no way to test this immediately. Caveat emptor, but this ought to work.