Dynamic hide select list on safari

Perhaps I'm doing it wrong, but here is the behavior I'm implementing on a select element :

I've created a page with several have a unic - its aim is to display a title like "Select your options".
To display my customized list and not the options list, according to the mains browsers compatibility, I had to implement a onclickfunction like this :

function showList(input,sIdTarget)
{
    //hide the dropdown list, compatible with all browser
    $(input).css({ "display": "none" }).blur().css({"display": "" });
    $("#"+sIdTarget).css("display","");
}

I still have an issue with Safari. Calling this function on the onclick event trigger it after an element of the list is clicked.

Here is a sample : https://jsfiddle.net/L6uhkg9h/1/

Thanks for your help.