If the battery voltage is the same it will probably be OK.
Things to watch for are whether the Cowon uses additional contacts to the battery. If you look at most mobile phone batteries you will see they have more than two contacts, one is positive, one is negative and the others are for data communication so the battery can report it's charge level. If the Cowon uses the communication contacts it will almost certainly not be compatible. If it just uses + and - you will be OK.
I suggest you buy a new charger for the phone battery rather than use one built into the Cowon, just in case the charge characteristics are different. You can do a lot of damage with a wrongly charged LiPo battery! Lots of sellers include a charger with the phone batteries.
Brian.