Usually it's easy to rewire the connector end. Not always, sometimes the end is potted. But then I cut off the end and try to reuse it, or source another connector. DB-9's are cheap and it's good to have a few spares around. Try to use heat shrink on adjacent wires, especially if the connector has a hood, it's possible for them to short when you cram in the wires and screw on the cover.
Yes. Before you start, take off the hood or cover, and take a picture or two. Check the colors before you start! Sometimes the OEM makes changes. Write down any changes if any. Then rewire as required. If you have some small diameter heat shrink put it on pins 1 and 3, (+5V and A) as a safeguard. It's not a difficult operation, you'll be done in far less than 30 minutes. It may take longer to collect the iron, solder and set up a small vise to hold the connector than to do the work. Good luck.
Assuming your documentation is correct, sure looks like it.
I also like the shield and included mounting bracket included with these scales a lot better than the Vevor units i purchased and only about $10 more in price.