Avoid the firing range?
I travel to the USA regularly for target shooting competitions... so lots of my clothes/gear would be well contaminated by residue from the smokeless propellants I use.. especially my range bag which has done double duty as my carry on... never had a problem.
I have even travelled with a powder thrower.. had THAT in my carry on (it's an expensive item and not terribly rugged) and presumably because it was an unusual looking thing they took it out of the bag and wiped the swab around
the interior of the powder reservoir....
NO result...
So.. from that experience.. I wouldn't be real concerned about flying after being at the range!