Also I see no reason to worry if you are holding a small amount of bitcoin in these wallets. But if you are holding some serious amount of bitcoins then it is recommended to use a hardware wallet.
That's 100% wrong, you don't have to download whole blockchain or run in prune mode. Blockchain size is still about 80GB for now, not 300GB.
There's lightweight wallet which some people call it as SPV (Simplified Payment Verification) wallet which allow user to use bitcoin wallet on desktop/mobile without download whole blockchain such as Electrum, Multibit and Mycelium.
The apps are very light, very easy to use, more secure than most online wallet and you have full control over your bitcoin.
Even you only have small amount of bitcoin, i would recommend you to use desktop/smartphone wallet.