I took a quick look at the standalone server for axis and I didn't see any obvious conflicts. I would backup your axis installation and then run this command line:
java -jar myna-1.0_beta_9.war -m upgrade -w $AXIS_HOME/webapp/
Assuming $AXIS_HOME points to your Axis installation. This will unpack Myna into the webapp folder. This is effectively the same as renaming the war file to .zip and unzipping it in that directory. However this method is preferable for upgrading in the future.
If this breaks Axis you could try running them side-by-side in a servlet container like tomcat. Or, if you are looking for something simpler and more portable, check out the Winstone Servlet Container[1] which can run arbitrary servlet apps from the command line with no setup.