Yes, you can use MEW to send SWT tokens just like any other ERC-20 token.
The Swarm City DApp is built on the Ethereum blockchain and therefore, requires ether to fuel the transaction. Users will need a small amount of Ether in the wallet holding the SWT to cover the gas transaction fees. To add ether to your wallet simply send ether to the public address holding the SWT.
Users do not need to move their SWT to a MEW paper wallet to use MEW to send SWT to other users. The Swarm City wallet can be loaded using MEW using a private key.
Go to MyEtherWallet and use the private key to unlock your Swarm City wallet.
This link to MEW has detailed instructions on how to send tokens.