I'm a bit like you in that specifying HTML feels a bit funny. I always preferred to add attributes, etc. to an object(though it could be quite tedious before jQuery). Anyway, one still needs to specify some HTML but this is a bit better:
$('<a />') .attr('href', '#') .attr('id', 'myytplayerControlsMute') .css('margin', '5px') .text('Mute') .click(function() { e.preventDefault(); }) .appendTo('body');