What you do is insufficient. Have you ever played with nmap? It is capable of guessing the operating system by probing the TCP implementation.

If you really want to get away with this, besides the legal problems, you will want to make a windows machine proxy everything while doing the actual calls to the apache server.

However, I must agree with the other comments about legal issues.

If your client failed to specify acceptable platform software, you might get the money by legal moves and then your client will have to pay for a second copy that complies to their new, accurate specification.

In general, I consider proper specification and acceptance criteria vital to any code-for-hire development, and most development in general.