Currently there is only paper wallet as a way to use it on devices that are not connected to the network from creation of private key to operation.
However, in order to withdraw money even if you can deposit money, you must enter the secret key into the software connected to the network.
I think that it is TREZER of hardware wallet that seems to be realized most quickly.
TREZER will correspond to the secret key of NEM.
By using here, remittance becomes possible without passing the secret key to the device connected to the network.
A lot of software related to NEM is currently being made. Software that realizes cold wallet will also come out.
Finally, I have never used a light wallet, so I do not know the difference.
And because the light wallet has not been updated, the wallet that corresponds to the latest feature becomes NanoWallet.
thanks