I just looked at the manual for your unit and if what I see is correct you should not have a lot of trouble hooking your old Bose speakers to the new system.
It looks like one end is a special connector, that goes on the DS400 side, and are color coded to match the channel for the speaker. However, it looks like the other end is just bare wire, the end that hooks to their speakers, the instructions show it as bare wire anyway.
If this is the case, then use the bare wire end of the speaker wire they supplied and twist each wire on to one of the bare old wires.
So say you are doing Left Front, pick the wire with the connector with the right color for Left Front, on one end there is the connector and the other the bar ends. Now get the Left Front bare wire from the Bose speakers and twist one wire together, of the two from the wires from the Bose, and then repeat on the second wire, we can work out polarity later.
MAKE SURE THE TWO WIRES CAN NEVER TOUCH!! Use electrical tape to carefully cover any bare wire.
Test it out, repeat for each set of wires you have.
If the ends are not like the manual at the speaker side and are wired right in to the speaker, then your last option is to cut off the connectors, about a good foot or more back from the end of the connector and then go back to plan A above.
Let me know if you are up to trying that and then we can talk how to determine polarity, don't worry it will not break anything to have the polarity wrong...