You say you want to sort on the first field only, yet you use -k 1, 3, which is sorting on 3 fields. Anyway, some untested code:

my $i = 0;
open my $fh, "input_file.txt" or die;
open my $oh, "> ss.txt" or die;
print $oh map  {(unpack "NNA*", $_) [-1]}
          sort
          map  {pack "NNA*", (/(\d+)/) [0], $i ++, $_} <$fh>;
close $fh or die;
close $oh or die;
rename "ss.txt", "input_file.txt" or die;
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