First, $2k is nothing to worry about. Bring it in cash if you want.
There are onboard ATMs. You can also bring travelers checks with you.
I am not sure on Carvnival, but on Princess you can just charge to your room, with no fees. I charged $8k on a recent cruise…. Tons of miles. lol.
If you want, you can pay it off before cruise ends, or just keep the cash and earn the miles.
On princess, you can charge $5k per day, up to $100k I believe for the total cruise, with no fees.