Subwoofer - is there one that would work in this situation?

Everyone is gonna say you need two.  Two are better.  But one is better than zero if you can adjust the roll off and volume to 'barely there'.  I had one single sub exactly where you describe in a Salamander three wide cabinet under the TV.  Even had a door with acoustic panel in front of it and it worked fine.  Good luck!

I think you will struggle with a single small sub in a locked location. DSP for the sub through internal or external like a Mini DSP would really help. 
 

if you plan to just come in under your mains, say 40hz or less, one can be ok. If you want to do a proper highpass at 60hz or higher two is much better/needed. 

Boxing in a sub sounds is a recipe for disaster. Adding vibration to your other equipment in the same shelf? No No Nanette!!

Buy the smaller REL T5x I use. I can be hidden many places.

Mr. Chesky's -6dB minimally controlled sub-bass speakers are extremely forgiving of room placement simply because they don't output frequency low enough to excite a rooms bass modes.

A properly positioned and optimized -3dB subwoofer can provide the delicate subsonic presentation for almost half the price. Some offer remote dsp control and a few customizable presets to compensate for Cheskey's or your own personal taste. Way more fun.

IMO, you’ll be wasting your time and money adding a subwoofer to those beautiful Janzens. Those speakers go down to 30hz +-3db. Adding a sub might ruin what you have!