I had a very similar issue and I'm not quite sure what you're having a problem with, as your suggested code worked great for me. It immediately (a requirement of yours) triggers the following change code.
$('#selectField').change(function(){
if($('#selectField').val() == 'N'){
$('#secondaryInput').hide();
} else {
$('#secondaryInput').show();
}
});
Then I take the value from the database (this is used on a form for both new input and editing existing records), set it as the selected value, and add the piece I was missing to trigger the above code, ".change()".
$('#selectField').val(valueFromDatabase).change();
So that if the existing value from the database is 'N', it immediately hides the secondary input field in my form.