https://bitcoin.org/en/choose-your-walletDownload Electrum from the above link and put your wallet.dat into the wallet directory, and log in. You'll avoid both fees, and any problems with trusting a third party with your coins. Electrum doesn't require the blockchain being installed locally and therefore you don't need to wait for it to sync.
First of all, there is no such thing as logging into your wallet.
Secondly, Electrum does not support wallet.dat natively. If you want to use Electrum, you have to extract your private keys and then import it into Electrum. The whole process doesn't require the synchronization of Bitcoin Core.
Spend $50 on a RDP with a fast download rate as I'm guessing your connection isn't good or its to expensive to download that much.
My reply:
Why risk your wallets?