Flux indeed. If it's a rosin based solder you can use a Q-tip and anything over a 90% iso-alcohol (less than that has too much water in it). If it's water based flux you would use... you guessed it, water! If it's brown then it's probably rosin flux.
Which solder type... size, tin/lead ratio, flux percentage are you using? Many new flux types are non-corrosive and could be left there. However, if you live in a warm/hot and humid climate it should be removed. A .031" diameter should be fine for these builds. Any larger could result in too much solder and excess flux.
See my soldering article in "Resources", especially if you're having trouble sleeping
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Joe G