Can I change wallet without shifting funds
Yes you can, depending on what version of multibit you have, you can do the following :


Multibit HD: You should have the backup seed words. You can directly use those seed words / master public key to create a new wallet like mycelium/electrum
Multibit Classic: Export out all the private keys https://multibit.org/help/v0.5/help_exportingPrivateKeys.html. You can import these private keys into the new wallet