Take a look at the documentation for the jQuery load function: http://api.jquery.com/load/. You can pass a callback that will fire once the load finishes, and from there you should be able to initialize the colorpicker (and only the ones within the result container):
$('#result').load("field_constructor.html #constructor", function() {
$("#result .colorpicker").spectrum({
color: "#f00"
});
});