$ cat textdata
This is line 1
This is line 2
This is the data I want replaced >>11111111<<
This is another line
etc etc until end of file.
$ printf "%s" 22222222 | dd conv=notrunc of=textdata seek=65 bs=1
$ cat textdata
This is line 1
This is line 2
This is the data I want replaced >>22222222<<
This is another line
etc etc until end of file.

#!/bin/bash

exec 5<hugedata
exec 6<>hugedata

# Read lines one at a time from both file descriptors.
# When we find the line we want in FD 5, FD 6 will still be at the
# previous line, allowing us to overwrite the line with it.
while read -u 5 LINE
do
        # Match strings like >>12345678<< anywhere in the line
        # save it in BASH_REMATCH in three segments:  ...>>, 11111111, <<...
        if [[ $LINE =~ ^(.*\>\>)([0-9]+)(\<\<.*)$ ]]
        then
                NEWLINE="${BASH_REMATCH[1]}22222222${BASH_REMATCH[3]}"

                if [ "${#NEWLINE}" -ne "${#LINE}" ]
                then
                        echo "Error, new line would be different length"
                        exit 1
                fi

                # Overwrite the line with a line of same length
                echo "${NEWLINE}" >&6
                exec 6>&-
                exec 5>&-

                echo "Found and replaced ${BASH_REMATCH[2]} with 22222222" >&2
                exit 0
        else
                read -u 6 LINE  # Keep FD 5 and FD 6 in sync
        fi
done <&5

echo "Warning, didn't find any data to replace" >&2
exit 1

$ cat hugedata
This is line 1
This is line 2
This is the data I want replaced >>11111111<<
This is another line
etc etc until end of file.
$ ./datarep2.sh
$ cat hugedata
This is line 1
This is line 2
This is the data I want replaced >>22222222<<
This is another line
etc etc until end of file.
$

( sed 's/orig/replacement/' < header ; cat restoffile ) | programusinghugefile