So the next step would be just to transfer all Leocoins from the old wallet to a new one?
No, not entirely. Migration can be done on an exchange, where your deposited coins will be migrated into new ones, that you then can trade or withdraw into the new wallet. If you chose to do the migration yourself, you should (a) download the new wallet and let it synchronize; (b) make a new address and a back-up; (c) go to
https://upgrade.leocoin.org/ and follow migration instructions there. The whole procedure does not take long, but if you wish to trade on an exchange after migration, please take care that they run the new wallet version too.