Just make sure that your lips are touching the top of the rim from the start of the sip until the end of it. This might require you to lean over the cup at the start and end and drink like a deranged pigeon with lips, but it will prevent drops on the outside of the rim.
Coffee gets a lot of nerd thought …
Look at this of how a drop of cream hits hot coffee and why.
But this is the bit on coffee ring research that I thought might have something to do with this, if coffee indeed does this more than any other liquid.
Dribblet?
Personally, when I add cream to coffee I let it stir via Brownian motion. It’s cool to watch how it distributes itself, and is a model for the heat death of the Universe, so there’s that.
That’s a straw, man. 
Liplet. Muglip. Mugdrop. Muglet. Rimdrop.