First right click on DOOM II in your library and select "Properties"

Then click on "Set Launch Options"

Here you can get Steam to launch whatever exe you want by including the path to that exe followed by %Command%

Download something like GZDoom and have the launch options set to something like
The exact way that I have mine setup is like this:
I have GZDoom installed into my Ultimate Doom install folder (renamed to dosbox.exe) and then give it an iwad parameter to have it load the doom 2 wad. Depending on where everything is for you you'll want it to be different.