DIY SMD - options for covering exposed vias?
Recommended is a trace length 'L' to via of at least 5 mils, with a solder mask dam along the length L. 



Otherwise you should use 'tented' vias (covered with solder mask), or offset plugged or blind vias. 

The main concern is the via sucking the solder away from the joint. If you've followed reasonable design rules, you may not have a shorting problem. 



Edit:

If you want to try coating the vias, you can get UV curable solder make in small quantities on eBay. Being UV rather than solvent base, it should be fairly low viscosity, and thus go down thin. I have not tried this, but at a few dollars it might be worth a try. You'll need a UV lamp to polymerize the coating.