Without messing with the DOM after table load, I don't think there is a way to "change" the markup datatables generates for the filter without hacking the datatables plugin itself.
However, one decent alternative would be to simply implement your own search filter.
To make a custom filter OUTSIDE the datatables markup:
Step 1:
Omit the 'f' portion of the sDom parameter: https://datatables.net/usage/options
Step 2:
Write your own markup for a search field
Step 3:
Use something similar to the accepted answer for this question to actually filter on your own custom search field: Datatables - Search Box outside datatable
Otherwise, you're left with just making custom css rules for the markup generated by 'f' and/or moving it around.