It seems possible ,not that your bitcoins are stuck in the network if it has reached the minimum number of conformations.Do you mind posting your bitcoin address or TXID ? Also you don't really have to download the entire blockchain to access the wallet I guess.
In the Electrum window, click Wallet -> Private Keys -> Sweep. Paste the private keys from Bitcoin-Qt here. Check the resulting transaction is okay and click Broadcast. Your funds will be swept from the addresses in Bitcoin Core and put in an Electrum wallet address.