easier still-
very few 'survival radios' (if any) use Li-Ion cells. . . .
take the old battery out. Count the cells. Most rechargable units (except LI-ion) are multiples of 1.2-1.4 volt cells.
In this case, 3 cells = 3.6 nominal volts, which is pretty standard for portable phones.
take the old pack to the local electronics shop, drugstore or (shudder!) radioshack (if you're in the states) and pick a new set that looks close. you'll probably need to splice the old connector onto the new battery.
be careful with the soldering iron so as not to overheat the cells if you must solder to them. use a big iron and work fast. . . 10 sec of heat is probably ok, 20 sec is not.
Just in case anyone is wondering: DO NOT USE ACID CORE SOLDER on batteries or electronics!
or:
take the unit outside in the sun, and turn it on.
measure the voltage developed by the solar panel across the battery connector. choose a battery that aproximates that value and will fit in the space.
many vendors out there. . . . by preference, use NiMH. (best long term durability vs sensitivty to charge parameters. I have a cheap set that are in daily use with 7 years on them.) Most of the big electronic supply houses and surplus outfits deal in rechargable batteries. ex: Newark, Allied or Jameco electronics.
-Dan
