Keep your wallet address outside of Bitcoin Core
Yes, you can use this architecture if Bitcoin nodes that you do not control do not know the private keys for all the addresses you use.
What you want to do is use a reputable library like Electrum Client, but there are many libraries in a variety of languages that can be used to accomplish basic tasks.
For example, in the Electrum client you can:
- Create address (wallet, keep private)
- Create a raw transaction (unsigned, basically a collection of utxos)
- Sign the transaction (keep your private key private), the output hex of the signed TX is safe to broadcast.
- broadcast deals
The Electrum client is also known as SPV mode (Simple Payment Verification). This is the protocol used for light clients, mobile wallets, etc.
When you sign a transaction, it may be broadcast via an uncontrollable Bitcoin node, a public Electrum server, or an explorer that provides relay through an API. Some mining pools also offer transaction broadcasting.
The most important thing to be extremely vigilant about is keeping your private key (wif) secret.
To get a “callback” for a transaction to your wallet, you can use Explorer to poll the address for a new transaction. And you can do all of this with the Electrum Wallet.