I'd opt for polymorphic constructors. You're initializing the same fields two different ways, from two different sources. Let your constructor examine the object being passed in; if it's a database handle, use that, and if not, see if it has the fields you want.

Here's a simple sketch:

package MyApp::Ticket;
sub new
{
    my ($class, $from, $extra) = @_;
    if (UNIVERSAL::isa($from, 'DBI'))   # it's a DB handle
    {
       my $sth = $from->prepare(...);
       $sth->execute($extra);
       # and so on
    }
    else
    {
       $self->{_time} = $from->{time};
       # etc.
    }
    bless $self, $class;
}

#  Called like so:

my $dbh = DBI->connect(...);
my $dbticket = MyApp::Ticket->new($dbh, $ticketno);

# or like so:
my %args;
my $ticket = MyApp::Ticket->new(\%args);
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Update
Better to use isa() instead of can().