How to remove button from Highcharts

Try adding exporting: { enabled: false } to your chart generation.

The best way to replace the hamburger icon is to disable the navigation buttonOptions, then create your own menu and customize the context one by one as stated in the documentation. From here you can use any icon you want with your own dropdown menu.

This disables the hamburger icon.

navigation: {
buttonOptions: {
  enabled: false
  }
 }

This is how you customize export options for your own list.

$('#print').click(function() {
chart.print();
});
$('#pdf').click(function() {
chart.exportChart({
  type: 'application/pdf',
  filename: 'my-pdf'
 });
});
$('#png').click(function() {
chart.exportChart({
  type: 'image/png',
  filename: 'my-png'
 });
});
$('#jpeg').click(function() {
chart.exportChart({
  type: 'image/jpeg',
  filename: 'my-jpeg'
 });
});
$('#svg').click(function() {
chart.exportChart({
  type: 'image/svg+xml',
  filename: 'my-svg'
 });
});

jsfiddle

Check this to create new button:

Example: http://jsfiddle.net/fXHB5/3496/

exporting: {
    buttons: [
        {
            symbol: 'diamond',
            x: -62,
            symbolFill: '#B5C9DF',
            hoverSymbolFill: '#779ABF',
            _titleKey: 'printButtonTitle',
            onclick: function() {
                alert('click!')
            }
        }
    ]
}