This may seem like a no-brainer, but I'd like to know the risk of wiping sweat from my brow with my forearm, or touching the hair on my head, etc. I'm not too excited about having to sanitize those, too. : /
Hair can serve as a defense against microbes, but...
Just ran a search on "sweat inactivation of viruses", and it came back with a link to an article published in Nature from an NIH website*. The original SARS-CoV-1 actually was found in sweat glands in people who were infected and had died from it!
This likely means the new virus will behave in much the same way. The only reasonable conclusion to draw is that anyone who is infected can shed virions not only by mouth and nose (and possibly feces), but also by skin contact anywhere on their body. Based on this article, one must assume that it can be spread to your arms etc. from other's sweat, until proven otherwise.
The original "no hand-shakes" notion was due to infected people rubbing their noses etc to contaminate their hands, and transmit it that way. Maybe there is more to it than that. We might want to pitch bare-elbow bumps too!
You have to wonder about all those guys in the NBA crashing into each other, with all that sweat pouring off their skin. Avoid any contact sports for sure. No pick-up BB games for quite a while. Heavy breathing from an infected individual in any sport could also be a potential source, not just coughing and sneezing. Go with golf for the foreseeable future. Fishing is actually a better idea!
So, if you are going out where a lot of people will be milling around, seems best to wear as much skin coverage as possible, based on this data. This may seem a bit extreme, but an infection from this virus can lead to other extremes as well.