Disable highcharts tooltip on certain lines, leave it enabled on others?

Use enableMouseTracking. It's the best way to do it.

Per Serie

series: [{
    name: 'Serie1',
    data: [7.0, 6.9, 9.5, 14.5, 18.2, 21.5, 25.2, 26.5, 23.3, 18.3, 13.9, 9.6],
    enableMouseTracking: false
}, {
    name: 'Serie2',
    data: [7.0, 6.9, 9.5, 15.5, 15.2, 15.5, 15.2, 15.5, 11.3, 17.3, 11.9, 9.6]
}]

Global

plotOptions: {
    series: {
        enableMouseTracking: false
    }
}

The code above will display tooltip for only the first serie.

Reference: enableMouseTracking

UPDATE

use enableMouseTracking: Boolean

Notice enableMouseTracking: Boolean was introduced after this question was asked

Old Answer

I just Disabled the heights point in the Tokyo series

here is your code

         tooltip: {
                formatter: function() {
                    
                    if(this.series.name == 'Tokyo' && this.y == 26.5 ){
                      return false ;
                    // to disable the tooltip at a point return false 
                    }else {
                        return '<b>'+ this.series.name +'</b><br/>'+
                        this.x +': '+ this.y +'°C';
                }   
                }
            }

jsfiddle