To answer your question directly: No, I am not sure how to change the port without using Server Network Utility.
But, will you need any ports open? If I understand you correctly, you will be using MSDE from a local application on the same machine. Will you have anything remote accessing the MSDE database on the local machine? If not, you will not need port 1433 open. That port is only needed for remote TCP connections to MSDE.
In fact, if you accept the default MSDE installation, all network connections will be disabled. Only Shared Memory connection will work, which do not use any network ports, and are much more efficient and quicker. For a local application, that is the better connection protocol.
So unless you need to modify the default MSDE installation for remote network connections, you will not need to modify the default port.
Hope this helps