Use below CSS to disable search box hover border color

input[type=text]:focus, input[type=text]:hover	{
    outline: none !important;
    border: none !important;
}

To disable in all input fields, use below css

input:focus, input:hover, 
textarea:focus, textarea:hover,
select:focus, select:hover {
    outline: none !important;
    border: none !important;
}