This is may be old post but I am posting it if it helps for others.
- Disable Drag and drop functionality
- Remove "or drag files here" from the +new document or drag files here.
use the below script by adding to each page as script editor or add it to master page.
<script type="text/javascript" src="http://code.jquery.com/jquery-
1.11.1.min.js">
</script>
<script type="text/javascript">
ExecuteOrDelayUntilScriptLoaded(function() {
g_uploadType = DragDropMode.NOTSUPPORTED;
SPDragDropManager.DragDropMode = DragDropMode.NOTSUPPORTED;
}, "DragDrop.js");
$(document).ready(function(){
if($(".ms-list-addnew span:eq(1)").text()=="new document"){
$(".ms-list-addnew span:eq(1)").closest("td").html(function(index,oldhtml){ return oldhtml.replace('or drag files here',''); }); }});
</script>