Back on topic. I don't swirl or try to dump trub/yeast from the spigot.
If I were to do anything, I'd try to swirl and tip/store the bucket so that the spigot is on the high side (moving the trub/yeast away from the spigot) during chilling. Tipping the bucket so the spigot is on the low side runs the risk of undue pressure on the spigot--I've had a few (incompletely) crack along the bulkhead portion and begin to leak--thankfully no significant loss of beer occurred, but I can see a situation where a complete crack in the bulkhead portion of the plastic spigot would cause you to lose the entire batch and make a horrible mess. Use the rubber washers on both sides (ideally) and hand tighten, but don't over tighten. Some spigots are better quality than others (e.g., better plastics)--some even allow you to attach a bottling wand directly to the spigot and some have plastic barbs that allow you to attach a tube. The later tend to be more inferior plastics that will easily crack (especially when cold--i.e., 34 F) if you are too rough with attaching a tube to the spigot. On these more fragile types of spigots, I recommend that "every action have an equal and opposite action" in order to attach the tube onto the spigot, i.e., push the spigot onto the tube as much as you are pushing the tube onto the spigot--net force on the bulkhead of the spigot is zero.
I take the 3-piece air lock off carefully (if you leave it on, you'll suck in the vodka or sanitizer solution) and place a plastic shot glass or plastic solo cup upside down over the airlock hole in the lid to prevent any airborne bacteria or yeast from potentially contaminating the beer. It also allows air pressure equalization during transfer. I then take the chilled fermentor bucket right out of the fridge and set it up on the counter.
I rack straight from the spigot (slow speed recommended)--don't open full blast if possible--keep the "suction" effect to a minimum in order not to disturb the yeast/trub cake. You may get a chunk of yeast that has collected in the spigot initially, but it clears quite rapidly. I often collect the first half cup of beer/yeast/trub out of the spigot for FG readings anyway--then it is on to transferring clear beer into the keg or bottling bucket. Use a hose to minimize oxygen exposure of the finished beer-- place the bottom of the hose in the recipient bucket or keg.
At the end of transferring, I can harvest the top layer of the slurry into a mason jar or bottle. After I get a 1/2 to 3/4ths of a mason jar's worth, I stop. The rest gets dumped out unless I plan to rack another beer right onto the yeast cake within a week or two.