If your phone was tied to your iCloud account, you can log in to iCloud using the same Apple ID as the one on your phone, and remove the phone from your Apple ID account and erase all the data on the phone. There are several relevant pages at Apple's support site:
Find My iPhone Activation Lock
If your iPhone, iPad, or iPod touch is lost or stolen
iCloud: Erase your device
iCloud: Remove your device from Find My iPhone
the URLs for the last two items are US-specific; if you're not in the US, there may be different rules
If/when the iPhone is recovered and reconnects to the Internet, the erase instruction from iCloud will erase all your personal data from the phone - credit cards, personal settings, email, contacts, calendars, purchased apps/music/movies, documents.
Since the phone currently doesn't work and you're planning to send it somewhere, erasing your iPhone will wipe all your personal info off, including credit cards. Removing your iPhone from your iCloud account will remove any application block, so anyone who gets it working can activate it as their own. That might feel risky, but whoever works on it will need full access to confirm that the repair worked.
If you take it to the Apple Store, their standard fix for water-damaged iPhones is to replace, rather than repair. What the charge will be depends on your warranty coverage. If you have the AppleCare extended warranty, it includes two matching replacement devices (i.e., a 64GB iP6 in exchange for a dead 64GB iP6) at a subsidized $79 each. If you bought the original phone with a credit card, check with the credit card company; a lot of credit cards include damage protection for purchased items, so they might provide some insurance coverage for this accident.