First of all note that being non-custodial isn't enough. If you want your fund to be secure, you should use a open-source wallet.
For example, both trustwallet and exodus are are non-custosial (which means they give you full access to your keys). But they are not secure. Because we don't know whether the keys have stored on their server or not.

One of the best choices is electrum.
It's open-source and non-custodial (which means it gives you full control over your keys)
One of the best features of electrum is that it allows you to make transactions offline (Means that you can sign the transaction on an offline device so your keys don't touch the internet.)