i think your probably ready to bottle as is, but to play it safe give it another week and bottle. I wouldn't personally swirl the beer any more just to prevent it from getting oxidized. Cold crashing won't stop bottle bombs, if there is fermentable sugar than the yeast will end up eating it. All you do by cold crashing is decrease the number of yeast in suspension.
In regards to the bottling right out of the spigot I am not sure on that. No experience but I would personally move it to another bottling bucket if available otherwise I would personally just bottle from the primary after adding your priming sugar, just my 2 cents.