Kip
... as an electronics technician for a couple of decades, who has designed and built a hundred projects, and as a certified video engineer and certified telecom technician, I can tell you will absolute certainty that there is no certain answer.
Only the schematics of the power supply and associated circuity will offer clues. Specifically, you will be back-feeding the power into the source. If the traces you mention are indeed just wire (no active or passive components) and if they go directly to the battery terminals, then you may be in luck.
You may be luckier than I at guessing circuitry. (Or perhaps a repair shop might provide the schematics [if they have them].) I have been surprised by what I find inside, sometimes, and by the logic that they used to build it.
The choice to go ahead might depend upon whether you can accept the potential consequences of failure, which can of course include losing your present processor.
Yes, it is a pain to reprogram a system, especially when some of the details are not known to you.
When I faced this same dilemma recently I explained in writing the options to the client. They can decide how much risk they want to take and how much money to spend to minimize that risk. I often make the mistake of assuming risks that really are the owner's. But I'm learning!
Best,
Mike