In light of this, I want to know if there is any other way to store bitcoin besides downloading the core. And which is safer.
There are many other secure wallets you can use to store and send bitcoins. Your choice will depend on;
• If the wallet is non custodian and if you are peculiar about autonomy (which you should be),
• If you intend to buy and hold altcoins along with Bitcoin, some wallets are exclusively for Bitcoin,
• If the wallet is open source and verifiable.
Electrum hits two out of the three points cause it is non custodian and open source.
How safe you wallet is depends on how you interact with it.