ViaBTC's free transaction accelerator doesn't accept transactions with less than 10 sat/byte fee. So your claim seems unlikely.
If this was my transaction, i'd probably do a CPFP if i needed the funds in a short timeframe or if i didn't trust the sender. If i trusted the sender, and i wasn't in a hurry, i'd just wait it out (and keep rebroadcasting the raw, signed tx)
This is the way to go, but it may depend on your wallet whether or not you can spend an unconfirmed transaction already.
If you can: the transaction is 5565 bytes, your new transaction will only add a few bytes. To get it to confirm within a few hours, you'll need to use roughly 0.001
BTC in fees. If you're willing to spend that, you'll also help confirm a couple dozen other withdrawals in the same transaction.
Considering how much exchanges usually charge for withdrawals, I'm curious why Bitstamp uses such a low fee (0.00015933
BTC for 5565 bytes)!