Yes, it's possible. Just create your own button and after click call chart.drillUp() function. See docs.

Highcharts v5 and v6: In Highcharts 5 classes were added to every element on a chart, so we can simply hide the button:

.highcharts-drillup-button {
  display: none;

Highcharts v4:

To disable default button, set text to empty string, see:

    lang: {
        drillUpText: ''

Related Query

More Query from same tag