How do I get around that?
With any half-decent schematic capture program you can design your own components, if you can get the data sheets for the components you are in business.
Can I use any of these programs to create a schematic of the traces and components of this board,
None of them will do it for you, but you can reverse engineer the board by looking at the traces and redrawing the circuit yourself. Just hope that it's only a 1- or 2-layer board 
If it's 20 years old I would suggest however that physically replicating it is not the way to go, just replicate the functionality with newer hardware. But that depends on it's exact function, it may be that there are no better chips even now, especially if there's no CPU involved
Rob