Admittedly just for my own fun I did it via a database (postgres 12.0). Don't do this at home --- although it isn't actually too bad, and only /just/ a bit more than a one-liner... I added the missing column names as I assume they are normally there in the real data.

#!/bin/bash

echo "CAT_HEADER,SUPPLIER_CODE,CUSTOMER_CODE,F4,F5,F6,F7,F8
CAT_LINE,0001P,ABC12345,20190924,,1,Z,3.36
CAT_LINE,0002P,ABC12345,20190924,,1,Z,3.36
CAT_LINE,0001P,ABC23456,20190924,,1,Z,2.24
CAT_LINE,0002P,ABC23456,20190924,,1,Z,2.24
CAT_LINE,0001P,ABC34567,20190924,,1,Z,2.24
CAT_LINE,0002P,ABC34567,20190924,,1,Z,2.24" > data.txt

head -n 1 data.txt | perl -ne 'chomp; print "
drop table if exists pm11107044 ;
create table pm11107044 (" . join(",", map {"\"$_\" text"} split(/,/, 
+$_)) . ");";
' | psql -qX && < data.txt psql -qXc "copy pm11107044 from stdin with 
+(format csv, header true);"

echo "-- unordered data.txt:"
cat data.txt
echo

echo "-- ordered data:"
echo "select * from pm11107044 order by 2, 3" | psql -qX --csv   # | m
+d5sum
echo

# older psql doesn't have  --csv  (introduced in postgres 13); in that
+ case use: 
# echo "copy(select * from pm11107044 order by 2, 3) to stdout with (f
+ormat csv, delimiter ',', header true)" | psql -qX
[download]

Output:

./pm.pl 
-- unordered data.txt:
CAT_HEADER,SUPPLIER_CODE,CUSTOMER_CODE,F4,F5,F6,F7,F8
CAT_LINE,0001P,ABC12345,20190924,,1,Z,3.36
CAT_LINE,0002P,ABC12345,20190924,,1,Z,3.36
CAT_LINE,0001P,ABC23456,20190924,,1,Z,2.24
CAT_LINE,0002P,ABC23456,20190924,,1,Z,2.24
CAT_LINE,0001P,ABC34567,20190924,,1,Z,2.24
CAT_LINE,0002P,ABC34567,20190924,,1,Z,2.24

-- ordered data:
CAT_HEADER,SUPPLIER_CODE,CUSTOMER_CODE,F4,F5,F6,F7,F8
CAT_LINE,0001P,ABC12345,20190924,,1,Z,3.36
CAT_LINE,0001P,ABC23456,20190924,,1,Z,2.24
CAT_LINE,0001P,ABC34567,20190924,,1,Z,2.24
CAT_LINE,0002P,ABC12345,20190924,,1,Z,3.36
CAT_LINE,0002P,ABC23456,20190924,,1,Z,2.24
CAT_LINE,0002P,ABC34567,20190924,,1,Z,2.24
[download]

( Another (actually more appropriate) database way would be to read the data file directly as text via file_fdw. Maybe I'll have a go at that tomorrow. )

Edit: I just realised that --csv is in postgresql 13 -- the alternative for earlier versions is mentioned ( COPY (select ...) ... )