Bitcoin is stored in your bitcoin address,not in your wallet. You can import your address in any wallet software if you have the private key.If you don't lose or leak your private key,your bitcoin is safe. If not, you lose.
i recommand you to use the cold store mode.
What is the method you speak of and how do I conduct it? Is it as simple as importing a private key from one wallet to the other?
step1 you should have a computer which will never be online.
Step2 you install the wallet software campabile with the Os using USB. The Usb must be clean.
Step3 Import the address to your wallet with private key using usb.Then never use the private key on any online-computer.
done.
If you want transfer your bitcoin in your address to others.
Step4 Using an online software to create the tx raw data. I use brainwallet html pages.This step don't need the private key.
Step5 copy the raw date to the clean usb. Then copy the tx raw data to your off-line computer and sigh it with your wallet.
Step6 copy the signed raw data to usb. then copy it to blockchain.info to spread it.
done.