Although you could export your private keys from Bitcoin Core and then import them into a new Electrum wallet, you'd be missing out on a number of important features.
A likely better option is to create a new Electrum wallet, write down the seed (very important! it is your backup), and then send your bitcoins from Bitcoin Core to an address in your new Electrum wallet.
For example, one benefit of doing it this way is your seed backup: it is all you'll ever need to restore a corrupted/lost wallet. If you export/import your private keys, you can't use a single seed to backup/restore your wallet.
Also, just FYI, Bitcoin Core version 0.11 will (sometime around July?) probably include
pruning support. When enabled, it'll reduce the storage requirements by a factor of about 30x.