Well, I've had a habit of desoldering wires by heating them to the molten state then flicking them to accelerate solder away from the wires. Yeah, it's a dumb idea, but it prevents wicking if you do it quick enough. And no - that's not a recommended method.

 

I worked in an area where they did NASA grade soldering for the satellites we built, and I don't remember the assemblers being required to take any particular protections when they soldered.
A small fan to deflect the flux fumes, if you are sensitive to that, is all you really need.
And, of course, it's probably a good idea to wear protective googles if you don't normally wear glasses.

 

flicking them to accelerate solder away from the wires

That and striking the device with molten solder onto the bench work very well indeed. I'm always finding tiny balls and flakes of solder in strange places. It comes with the territory...

 

I use a solder sucker and braid, so I guess that is why I don’t see flying solder.

 

Shortcuts. That's all it is.

 

I use a solder sucker and braid, so I guess that is why I don’t see flying solder.

Oh I do too. In fact, I have a vacuum desolderer that I normally use for the "big stuff" that braid won't do quickly. But sometimes... I even put a cheap 5x8 "oriental" rug in front of my bench to catch all the crap that escapes it. Every time my wife vacuums my office where the bench is she leaves a pile of "treasures" she rescued while vacuuming.