Thanks for the info and opinions....
I've done some additional research and I think I have found an interesting chain that will fit the bill. It is specifically designed for non-shifting applications:
KMC
Z610HX (silver, bushingless); made specially for single-speed drivetrains - $15.00 At Business Cycles
http://www.businesscycles.com/trcomp.htm#chains
Below is the manufacturer's site. It appears that they make at least some of Shimano's chains.
http://rubber.24h.com.tw/mr86/kmc/speed/single.htm