You should use btc core wallet (desktop) it may not be a better option for speed of the transaction.
But you can customisze the setting under the options when you send to the bare minimum almost next to nothing if youre not in a hurry.
Even lite wallets contain that similar option wherein you could customize the fee that you are willing to pay. Transaction speeds are almost instant, the confirmation times from the network aren't. The only downside of not paying fees for your transactions to get settled is that you'll wait for a longer time than the usual for your transactions to get processed, which is fine if you're not in a hurry.