You can use the blockchain wallet on your smart phone, I think it is very safe to use a blockchain wallet or otherwise like a coinbase wallet
Online wallets are never secure nor safe you don't hold complete control over your Bitcoins, hence, there is always a chance that you will lose your funds (due to hacks, bugs, malwares, etc.). Better use an offline wallet, OP. It's much more secure and you have control over your coins something like Bitcoin Core (if you can bear/handle downloading more than 60GBs), or use a light wallet like Electrum.
Security depends on how users keep their bitcoins not just by looking at the wallets they use