Hmm, it does seem a bit strange that there isn't a Bitdepth setting for handhelds.
Aside from the converter idea, a couple of the Handheld Encoders allow custom settings, including command line settings. Maybe you can work something out there. Of course it depends what format you are placing in the Handheld folder for Sonos to use, whether command line commands are available.
Also, a quick bit of research on Bit Depth in MP3 files informed me that MP3 files don't actually have a Bit Depth, and it is the decoder that decides what Bit Depth to use. I didn't know that. So maybe if you can live with MP3s, perhaps at the "Extreme" quality setting, then maybe the Sonos will play the files without issue, at the Bit Depth that it can support, 16Bit.