Urgh, I finally got around to doing this, and it's not working out. I got a latching push-button switch, mounted it in the housing, cut the red lead from the battery compartment in the middle, and connected the red and black leads from the switch to the two ends. (Black to batteries, red to board.) Now what I've got is this: on first press of button, light switches on, but in lowest brightness. (The light has three brightness levels, switched by subsequent presses of the touch-sensitive button.) But after that, pressing the new switch does nothing, no on, no off, no level changes. When on, I can use the touch-sensitive button to turn on or off, but no level changes. If I pull batteries, then replace, first press turns on again, but same result. I don't actually need the two lower settings, I'd be happiest if I just had the new button do on and off of highest brightness - but could accept new switch as power interrupt, and touch-sensitive switch as controller, as discussed. Could I just bypass the board and touch-sensitive switch altogether, and get simple on/off at full brightness by just leaving button black to batteries, button red to both bulbs, and black from bulbs to white from batteries?
One thing - the new push-button has four leads, as it's illuminated; one red, one black, and two blue. I assumed that the blue leads were to feed the led, and the black & red for circuit, so thought if I just taped off the blues, and used the black & red, it would work (I don't care about the led illumination). But as it is wired, the illuminated ring is on, so maybe I am mistaken? (I tried to find a simple two lead switch, but couldn't find one of the size and type I want, with pre-soldered leads - I wanted to avoid soldering leads to button myself.)