In Bitcoin Core, this was done simply-I delete the transaction from the mempool, and then conduct a new one with a higher Commission, as soon as it passed - the old one will not be held and will be discarded in any case by all nodes
The first transaction will not be deleted from any node beside yours until your second transaction is confirmed (which does not have to be the case!).
All changes you do to your mempool are exclusively local on your node.
So the question is how to delete a transaction in Electrum
You can not delete transactions from the mempool of all nodes.
You can create a new transaction spending the same utxo's with a higher fee. This can (but does not have to!) lead to your second transaction being included into a block.