Purely experimental and because it got me interested... and because you tagged jQuery... you COULD create your own virtual keyboard and hide it, then listen for each click event. You could then just use jQuery's trigger() function for any key you wish to simulate...
HTML
<div id="keyboard">
   <button id="char-65" class="keyboard">A</button> // A
   <button id="char-66" class="keyboard">B</button> // B
   // ......
   <button id="char-125" class="keyboard">}</button> // }
   <button id="char-126" class="keyboard">~</button> // ~
</div>
CSS
#keyboard{
    display:none
}
jQuery
$('.keyboard').on('click', function(ev){
     switch(ev.target.id){
          case 'char-65': // do whatever
          break;
          case 'char-66': // do whatever
          break;
     }
});
Then just trigger your buttons...
$('#char-65').trigger('click');
$('#char-66').trigger('click');
UPDATE:
Was looking around at better solutions and my answer get's totally owned by this
function simulateKeyPress(character) {
  $.event.trigger({ type : 'keypress', which : character.charCodeAt(0) });
}
simulateKeyPress("A");
simulateKeyPress("B");