How can I disable drag & drop for whole widget?

You can completely disable drag & drop with the following code:

uploadcare.plugin(function(uploadcare) {
  var $ = uploadcare.jQuery;
  uploadcare.utils.abilities.fileDragAndDrop = false;
  uploadcare.utils.abilities.dragAndDrop = false;
  uploadcare.dragdrop.support = false;
  uploadcare.dragdrop.receiveDrop = function(){};
  $(document).off('dragenter dragleave drop mouseenter');
});