^^ you are wrong because electrum is one of those wallets that has the option to replace by fee. and i have recently done one.
http://docs.electrum.org/en/latest/faq.htmlalthough don't expect your transaction to be replaced all over the network. the problem is that many nodes don't recognize RBF so they will ignore it and see it as double spend and keep your original transaction.
my experience was that it was successful because the miner picked up my higher fee tx fast and that is the only thing that matters.
and by the way you don't have to make another transaction, electrum is so user friendly about it. go to your history tab and click on the transaction and choose increase fee. easy!