Just look in src/hmenu.css for occurrences of "width: 18px" (should appear 2 times) and replace them with "width: 0".

Alternatively—a better solution if you don't want to modify the original files—you can put the following lines somewhere in your own CSS file (needs to be loaded after the DynarchMenu skin):

div.dynarch-popup-menu tr.item td.icon img,
div.dynarch-popup-menu tr.item td.icon div {
  width: 0;
}
div.dynarch-popup-menu tr.item td.icon {
  width: 0;
}

After this, if there are items where you would like to include an icon, you may put the <IMG> tag inside the <A> tag, but note that in this case it's usually impossible to achieve perfectly centered vertical alignment.