Create transaction with bitcoin core
Certainly. Bitcoin Core has various utility RPCs which are separate from the wallet. You can use createrawtransaction to create a transaction. Of course, without the wallet, you will need to specify the inputs and outputs for the transaction manually. You can sign that transaction with a private key not in the wallet by using signrawtransactionwithkey. You can then broadcast that transaction using sendrawtransaction.

To get the outputs for an address that you can use in createrawtransaction, you can use scantxoutset to scan the UTXO set for UTXOs pertaining to a particular address.

All of these can be done without the internal wallet and separate from the internal wallet.