The classpath for compilation is not necessarily the same as the classpath for the runtime. There is a launch version (Run-> Run ...) that will teach you what it is.
Please note that SWT-jar are just API classes. For real runtime classes, you will need the per-os binary, so it may be missing. If you add a container of class "swt", then it should do the right thing.
What is the contents of .classpath in the current project?
Alblue
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