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>Theoretically could you use an electron gun in a vacuum chamber to cause mutations in a seed?

Yes

That was one of the suggested experiments in the classic Amateur Scientist column "A Homemade Atom Smasher" (page 344 at http://www.sciencemadness.org/library/books/projects_for_the... ).

Spin up that old Van de Graaff in your closet and make some cool mutations!

Sure, I guess any mutagen would do, as long as you have some control over the dosage.

Mutagenic chemicals might work equally well. Would be super annoying/dangerous to work with compared to flipping a switch on an electron gun though.

The mutagenesis is not the rate limiting step, its the screening of positive mutants.