Ouch. This should be a bit faster. The trick is to do a quick first pass through and count the number of occurrences of each (1st) word, and then go through a 2nd time and output only those lines where $words{$1} == 1.

#!/usr/bin/env perl

use 5.012;
use warnings FATAL => 'all';

my %words; # Number of times word appears first in a string
my @lines = <DATA>;
chomp @lines;

$words{$_}++ for map { /^(\S+)/ ? $1 : () } @lines;
say for grep { /^(\S+)/ ? $words{$1} == 1 : 1 } @lines;

__DATA__
hello 1234 5698 7458
hi 1457 7459 6214
good_day 1458
hi 1258 3658
good_morning 4758
hi 1453
oneword
hi
[download]

Output:

hello 1234 5698 7458
good_day 1458
good_morning 4758
oneword
[download]