No, it will not hurt your preamp if you only use one channel. However, I don't think you need to use a preamp. The subwoofer output on your HT Processor should already volume controlled (just like all the other channels on the HT Processor output). You can connect it directly to the Bryston amp. Although I think there are be better amps. The Bryston amps tend to be a bit thin sounding on the bass/midbass.
That being said, it looks like your Wilson Benesch is a sealed sub. These tend to sound a lot cleaner. For home theater usage, I like to have a ported/vented sub because they sound thicker and more meatier. If you want to replace the Wilson, maybe look at a
Rythmik
vented subwoofer.
If you want a really nice sub amp for cheap, look for a used Emotiva XPR-1 "Gen 1" or "Gen 2" amp. I have found that these have some of the best bass (especially when you upgrade the fuses). A Parasound JC1 might be okay, but I don't think they are as good in the bass as the Emotiva. Alternatively, you can look at one of the higher power Class D amps.