Alex,
To remove the Statistics... option from the widget action menu you have to alter some widget code. In the SingleQueryResult.js find the _onBtnMenuClicked function and make this change (line 24).
_onBtnMenuClicked: function(evt) {
var position = html.position(evt.target || evt.srcElement);
var featureSet = this._getFeatureSet();
var currentAttrs = this.getCurrentAttrs();
var layer = currentAttrs.query.resultLayer;
this.featureActionManager.getSupportedActions(featureSet, layer).then(lang.hitch(this, function(actions) {
array.forEach(actions, lang.hitch(this, function(action) {
action.data = featureSet;
}));
if (!currentAttrs.config.enableExport) {
var exportActionNames = [
'ExportToCSV',
'ExportToFeatureCollection',
'ExportToGeoJSON',
'SaveToMyContent'
];
actions = array.filter(actions, lang.hitch(this, function(action) {
return exportActionNames.indexOf(action.name) < 0;
}));
}
actions = array.filter(actions, lang.hitch(this, function(action) {
return action.name !== 'CreateLayer' && action.name !== 'ShowStatistics';
}));
....