it will work. you answered your own question about the cables. you have one DB25 to DB9 going to your computer. new cables will be the same as this one.
on the DB9 DB25
2 2
3 3
5 7
now I do not know what you use for handshake
on your cables coming from the machine to the switch box (at the switch box end only)
check and see if 4 jumps back to 5 or if 6,8,20 are jumped together.
you should be able to find a pin out in the control manuals.