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!