A little OTT but the free Mach3 CNC would control P.P. outputs, the relay may be to high a current for a P.P. but you can use a 2n7000 to drive it with.
You could also use a COM port for RS232 if using a outboard μp. such as PICmicro or Arduino etc.
You may be better off looking at building a small application in C++ (or another language) to do this for you.
There are many 'Parallel port test' apps available for windows, they typically require the .Net framework, but I am not aware of anything that you could possibly do much 'custom' with aside from clicking it yourself with a mouse.
On second thought Hyper Terminal may not be much use on its own because it was basically designed as a DialUp app for intended Modem use.
Let me look through my VB6 files. Over the years I wrote quite a few MSComm (Serial Port) programs. I may have one already written that will fill the bill. Even if I don't (doubt it) it wouldn't take me very long to write it. I assume you'd like a button on the app to switch the pin High - Low? If you like I can give you 3 output pins with a button assigned to each. I will be using the DTR, RTS, and TXD pins. You will have to interface the pins with 3 transistors.