Well, that all worked nicely.
It was a pretty simple process (I managed to make it appear difficult though). I checked the PCB and the resistor value is 18K, which I also confirmed with the ohmmeter.
After purchasing a lovely domed momentary switch and drilling the side of the case to hold it, it then occurred to me that I had purchased a "normally open" SDST switch, but what I needed was a "normally closed" switch. [insert emoticon for "you bloody idiot" here]
I was amazed at how difficult it is to find a NC momentary switch of the right sort of size. I found one that was too big (long) to fit without fouling one thing or another, but ended up using a DPDT mom switch and just cut off the excess terminals. The only place I could find to fit it was in the base of the handle - which is no drama, as I only want to use it for programming cars and track calls.
As for the wiring, thath part was easy - simply desoldered the 'return' wire and soldered it to one of the switch terminals, then inserted a wire from the PCB to the other terminal, and soldered the 18K resistor across teh two terminals. So when the switch is closed (normal) the current flows freely, and when the button is pushed and the switch opens, the current is forced to travel through the resistor.
Thanks to all for your assistance.