Most airlines should be able to transport air pistols,I always inform them by phone that I will be checking one in,the only requirement is that the cylinders are empty usually,though a couple have refused to transport pellets,as they don't know the difference between pellets and ammunition,showing them some usually solves this problem.
Steyr LG110 Hunter,AA410 in Gary Cane stock,HC, Steyr LP50,Morini 164ei,Morini CM84e,Anschutz 1417 thumbhole,Rimfire Magic 10/22,Anschutz 1913,Rieder and Lenz Z2,Keppeler 6mmbr