Even if you don't want to use a hardware wallet for any reason, you don't have to keep your fund on an exchange.
You can use non-custodial wallets and have full control over your fund.
It's recommended to use a trustworthy open-source non-custodial wallet.
If you are on desktop, I recommend you to use electrum or Sparrow and if you are an mobile, I recommend you to use electrum or bluewallet.
Use Electrum wallet with either a single signature wallet or multisig wallet. Use strong password for your wallet (single signature wallet or co-signer wallets).
I prefer to use single signature wallet with strong password than multisig wallet because it will cost me me fee.
I don't recommend OP to use 2FA wallet in Electrum because extra fee will be paid to Trusted coin.