If you grab the coreutils from Gnutils you'll be able to do a lot of the stuff you can do with Cygwin without having to install cygwin.
Then you can use things like head, tail and cat which will allow you to do what you're looking to.
e.g.
head -n 4 file2.txt
to get the first four lines of file2.
Extract the zip from the page linked above, and grab whichever of the utils you need to use out of the bin directory and put them in a directory in your path - e.g. for the below you'd want mv, head and tail. You could use the built in DOS move command, but you'd need to change the options slightly.
The question is a little unclear, but if you're looking to remove the first four lines of file2.txt and append them to file1.txt you can do the following:
head -n 4 file2.txt >> file1.txt
tail -n +5 file2.txt >> temp.txt
mv temp.txt file2.txt