Your iRiver puts out something like 3V "Plug-in-Power" which will power the mics, and it should work. Will it work good? Will it overload? I can't say.
My suggestion is to get the better "Core Sound Binaurals" with the built in battery box (as opposed to the "low cost" ones you are probably looking at). They show up in the yard sale in the $100 range from time to time.