As you can see from the first URL, the battery and device are fairly long together, so -- as you can see from the second -- I snipped the battery connector off an old guitar tuner and soldered those leads to the device, and then I could put the battery in one place on the clock (there happened to be just enough room on one side) and the device in another. Tolerances were very tight.
The trick then was to get the clock to him without him realizing what was going on. I wasn't going to his house any time soon, but I happened to go trap shooting with him this weekend, and we went out to lunch afterward. I "needed" to leave early, so I asked for his keys to give him back the clock, and put the clock in his trunk and returned the keys to him.
And thankfully, he didn't hear the beeping as he put the clock in his office at home. It took him a couple of days to figure it out. The only downside is that his hearing is not as good as my mother-in-law's, so she got more annoyed by it than he did.
Now he says he is going to get me. Bring it, old man.