Use the exchanges sites wallets 
, bittrex is the best
, bittrex is the best Wait - so I could still transmit my "old" bitcoin from my wallet to bittrex and they will still be split today?
I was thinking that I would have had to send them to bittrex before August 1st to be able to use this methode.
No, absolutely not. If you transfer bitcoin (BTC, not Bitcoin Cash aka BCC, BCH, XBC) to any exchange today, you'll only be credited with BTC. You won't get the opportunity to get more Bitcoin Cash from that deposit.
On the other hand, if you had BTC in your possession (you held the private keys yourself at the time) during the fork, you should already have access to an equal number of Bticoin Cash BCC.
You're asking about moving regular, legacy Bitcoin (BTC) from your Blockchain.info wallet to another regular Bitcoin wallet (just not Electrum), right? So you're question doesn't involve Bitcoin Cash (BCC, aka BCH/XBC) at all? If so, you should just do this normally. Get a receiving address from your destination wallet, put that in the "Send to" field of your Blockchain.info wallet, and off you go.
Unfortunately, I haven't used Blockchain.info's wallet for a long time, so I don't know more specifics than that.