Somebody may know of a way to do it that I don't. As a workaround, have you tried extracting the park multiple times then deleting all but one ride in each of them?
Option 1:
Load the park in the editor. Unfreeze a coaster. Delete the coaster. Repeat until 1 coaster left. Exit editor, it won't ask to save changes. Ride the coaster.
You will have to do this every time you want to ride one.
Option 2:
Copy park directory from install path to your own parks, and it won't be Read-Only anymore.