I mostly use my hardware wallet to save most of my bitcoins where I have access to my private key.
However, I also keep a good amount of bitcoin in my online BlockChain wallet for quick trading transfers.
my question is, do I need to worry about my bitcoins I hold in my online wallet? Will it be safe? What can be the consequence of of August 1st network split on my bitcoins?
Can anyone please give me an answer?
I guess you know the answer to the question you asked because you asked only about the safety of the online wallet, not the hardware wallet. Meaning you suspect something could go wrong with your web wallet. As a Hero Member, you obviously have been here a long time and expectedly should be advising us. Anyway, let me tell you want I did: I moved my coins from an exchange to an Electrum wallet and then exchanged a few of my Bitcoin to altcoins of interest instead of selling off in panic. Don't sell off. Get them exchanged for altcoins!