use strict;
use warnings;

my %exceptions = (cust1 => \&cust1Handler, cust2 => \&cust2Handler);

eval {
    die "cust1\n";
};

if ($@) {
    chomp $@;
    die "Unhandled exception: $@\n" unless exists $exceptions{$@};
    $exceptions{$@}->();

} else {
    print "Success\n";
}


sub cust1Handler {
    print "Turned to custard - 1\n";
}


sub cust2Handler {
    print "Turned to custard - 2\n";
}
[download]

Prints:

Turned to custard - 1
[download]

may be what you are after. Note the newline magic to suppress the context text that die would otherwise add.

Or is your question if you can use Fatal for non-builtin functions? (if yes, just try it - I think it should work)

Note that Fatal does throw exceptions, though it's perhaps not obvious from the code that uses fatalized functions.

And what exactly do you mean with "customized exceptions"? Exception Objects? Or just different error messages?