Version 2.0 of Tyrian had a custom ship editor, but I don't know whether it can open existing ship sprites and save it into a file
Here's something that could work:
While playing press Alt+Enter (or WHATEVER that combination was ). Windows will try to disable fullscreen in the game. And then it finds out that doesn't work and the game hangs . Then you can make a screenie of it by pressing PrintScreen. Open a drawing program (Paint or something) and press Paste. (pressing PrintScreen while the game is still set to fullscreen usually gives nothing)