I guess there will be no problem. Loading LiOn batteries MUST be done with an intelligent device to control current and voltage.
If the battery doesn't have, the charging unit has to do it. In this case the iriver story is responsible. The most important thing ist the voltage level, which must not be exceed. Its depending from the type of battery (LiOn - LiPoly).
USB is only for delivering 5V and has nothing to do with charging control. I guess you already knew that, but perhaps somebody read this does not.
When I replace the battery I will do the first charging with open case and have a look at the temperature (I have an IR-meter).
Greetings from Sauerland, Thomas