If the contacts inside the switch are oxidized, there isn't much you could achieve by blowing into it other than making it worse.
http://gbatemp.net/threads/kipmudzs-solution-to-malfunctioning-dslites-shoulder-buttons.335590/
Youtube video shows you how to open it up and take out the L/R button switches. Judging by how they looked, I think you might be able to open the triggers up in a similar manner to the DS Lite's triggers. That should allow you to take out the rubber button and the metal cap inside the switch, so you can clean them out.
As always, when opening up electronics, don't force anything open; be careful. I am not responsible for anything if you broke something from being too rough
That being said, your R button already isn't really working, so even if you broke the trigger, it already wasn't working in the first place.
Otherwise, if you are interested, you can get replacements for cheap here:
http://www.amazon.com/Internal-Shoulder-Nintendo-3DS-replacement-packaging/dp/B00C9CBH5E
Thankfully, for the 3DS, the L/R buttons are on cables that connect to the main board, rather than triggers soldered directly onto the motherboard
that makes it much easier to replace them.