Why HE11 mode of corrugated waveguides would not be a natural source of axion field?
The source term for the axion is proportional to ##\mathbf{E}\cdot \mathbf{B}##. This quantity is suppressed by a factor of ##\lambda/a##, where ##\lambda## is the wavelength and ##a## is the radius of the waveguide. Looking around I found a paper suggesting that some of the waveguides involved in ITER have ##\lambda/a \sim 1/20##, so perhaps this isn't a huge suppression.
The original Sikivie paper is available at http://ccdb5fs.kek.jp/cgi-bin/img/allpdf?198309239 . Perhaps you can modify his eqs (6,7) in order to estimate the axion production in this situation.