I have concluded that chains wear by far the most when riding in the wet. So cleaning and lubing immediately after a wet ride is of utmost importance.
I use Prolink, a "dry" lube - it does not pick up much dirt. So it suffices for me to blow the chain clean using a cheap compressor which I bought mostly for cleaning my bikes. After a thorough blowing clean of the chain, relube and I'm ready to go again. So this is a method to avoid removing the chain.
For your Curve which does not have a derailer, just use Prolink or Rock'nRoll Gold, and wipe well after lubing - no further cleaning necessary.