The newest version of bitcoin core 0.12 introduced a feature called replace by fee. This can be used to issue a transaction with a higher fee spending coins that have not yet been picked up in a block.
I think he could use that to create another tx using the same inputs, sign and try to broadcast (send).
Reference: Bitcoin Core :: Opt-in RBF FAQ
Detailed walk-through: http://bitzuma.com/posts/how-to-clear-a-stuck-bitcoin-transaction/ (if the transaction is a simple BTC send, then no changes should be required; if it’s a Counterparty transaction, then one would have to encode the payload first and in that case the procedure would have to contain additional steps)
There’s no way to do that in CW I think. If you create another it just sends the same amount again (so as you say you may overpay if the both happen to end up confirmed).
This by the way is a good reason to keep the CW minimum tx free per kB at a reasonably high level. Of course it hurts as well, but it’s a tradeoff and skilled users can use other wallets to spend lower fees, but these zombie transactions are hard to deal with and certainly something that regular users find confusing. (I’m not saying CW doesn’t need a per-tx fee or per-tx priority setting, of course).
@ioglnx: Which tutorial is not accurate?