Perhaps a better choice with the 172 (1980) is to select 20 degrees. If you had to go around, there isn't as much drag at 20 degrees.
Now, you have to watch it with thinking that going slower gives you less control. Remember that lowering flaps lowers your stall speed. You want to do two things: 1) Fly to and through the flare under control, and 2) Touch down and roll out under control.
Now, if you are so slow that the application of full rudder is not enough to straighten you out (you may wish to test this on final), then you are landing in too much of a crosswind. My personal preference would be to select or request another runway, or land somewhere else. I am not going to land and "see what I can do."
Another point to clarify: do not add anything to your approach speed to compensate for a crosswind. Do not add anything. If you approach at 60 kts, you still approach at 60 kts. You add some airspeed for a gust factor, not a steady-state crosswind.
The other point to consider is that if you are used to 40 degrees of flaps, and you suddenly are using 10 or none, your landing attitude will be different. When you pull to the normal flare attitude, you may find yourself in a different world which, in turn, create more of a hazard for you than if you had simply used 20 or 30 degrees of flaps in the first place. Remember, too, that when you pull the nose up, it wants to go left. With no flaps or 10 degrees, your nose will be higher for a longer period of time, unless you force the plane onto the runway (bad idea).