Another way, using fixed-length I/O (and also avoiding use of a regex to step through the string byte-by-byte):

>perl -wMstrict -le
"{ local $/ = \10;
   my $fname = 'junk';
   open my $fh, '<:raw', $fname or die qq{opening '$fname': $!};
   while (defined(my $buffer = <$fh>)) {
     printf '%02x ', ord substr $buffer, $_, 1
       for 0 .. length($buffer) - 1;
     print '';
     }
   close $fh;
 }
"
61 62 63 64 65 66 67 68 69 6a
6b 6c 6d 6e 6f 70 71 72 73 74
75 76 77 78 79 7a 0d 0a
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Update: BTW: The test file was created with
    perl -e "print 'a' .. 'z', qq{\n}" > junk