That's probably a better bet than your bucket for the purposes of reducing oxygen exposure. The problem with a carboy is the safety issues with moving a heavy one around and the potential for breakage. But they are definitely better for letting beer sit.
I'll second the recommendation for getting a Fermonster. They are only slightly more expensive than standard buckets, and they have an o-ring sealing lid. You can also modify the solid lid pretty easily to add keg quick-release hookups. That let's you transfer directly to a purged keg and avoid all oxygen exposure entirely.
Lastly, you could also just let the beer clear in the keg itself for a few weeks. That's the same thing as a cold crash, you'll just have more yeast sediment in the keg than you would if you cold crashed in your fermenter. But doing it in the keg avoid oxygen exposure from suck back. After you pull a beer or two, you should clear out the yeast sediment from around the keg's dip tube. All that said, letting your beer sit on the yeast for at least two weeks has a lot of other flavor benefits beyond just settling the yeast out. So I would definitely start waiting at least two weeks before you keg.
