Simple. Keep your flies away from water until you're ready to fish with them.
Seriously, I have no interest in tying flies faster, but I do have an interest in tying easier and better flies if that means I can catch more fish with them. Along that line, when tying Adams, which is my all time favorite fly (parachute style), I keep a plastic container at hand in which I have pre-mixed muskrat fur for the body (mixed with a coffee grinder), the same as I do with practically all of my natural fur dubbings. This fur doesn't "float around" at all, even with the top off the container, and all I need do is take a pinch or two out as I apply it to the tying thread. Even though it takes time to pre-mix fur in this manner, it is much faster in the long run to do a large quantity at one time, than cutting fur from the skin, and mixing it in small batches more frequently. (When I first started tying flies, I only cut enough fur from a skin, and mixed it for dubbing for the one fly I was tying at the time, which takes forever.)
I'm not a fan at all of upright hackle tip wings, which take a disproportionate amount of time to tie anyway, and long ago have replaced them on all of my Adams with Z-lon wings, which are much faster to tie, and more effective, in my opinion.
I also bumble around a bit tying brown and grizzly mixed hackle barbule tails. These could be tied with one Cree feather, or with Coq de Leon barbules, both of which I sometimes use, but I've found that by pre-selecting one brown and one grizzly hackle of the same size barbule length, and then gluing the two hackles together at the butt ends with super glue, is almost as fast. I sometimes glue a batch of hackles together ahead of time.
John
p.s. There are a couple other fly patterns, one of which is the Morrish Hopper for example, that I found an easy way to save time. For the past several years I gone through quite a lot of Morrish Hoppers, and they are quite time consuming for me to tie. As a result, I've found that by making just a sinlge trip to the fly shop, and buying a couple dozen or so at a time, I save a lot of time!