I don't know about any laws in Panama on importing a gun. That said, the best way to travel with a gun is to simply say, "I have have a gun I want to check." Do not say it is an airgun -- just "gun." PCP airguns have tanks that may raise issues -- one tank can be attached to the gun (and should be!); the other tank should be sent via UPS or some other method. For pistols, I would have to read the airline and TSA screening rules, I think you can put the pistol in your checked luggage after declaration.
Something as obvious as a pistol should be in a large non-descript bag to discourage theft. The pistol box should be locked as should your luggage. (In both cases, use locks that are compatible with TSA rules!) Do not volunteer extraneous information, just answer questions relating to the gun (is it loaded?, etc.) Oddly, it is easier to travel with a firearm and ammo than with airguns, hence the suggestion of declaring a "gun" (airguns are not firearms by Federal rules).
Best,Joe in MD