Hi Hookpunch,

Just get a solar PV panel such as the Sunlinq type and appropriate battery charger which can take a 12V input to recharge the batteries for all your needs and not just the radio.
Freeplay Freecharge can also be used if solar becomes unworkable.

http://www.freeplayenergy.com/product/freecharge12v

Good high quality SW, AM and FM radios are avialable such as the Roberts R9921 or Roberts R876 or Sony ICF-SW7600GR which are designed to work with AA cells.

Cheaper models are available but don't perform as well especially on the coverage and the ability to discriminate radio broadcast channels for especially for World SW frequencies such as the BBC World Service.

Eneloop NiMh rechargeable AA type cells are preferrable as they keep their charge much longer i.e over a year. A set of AAs can be charging under solar while the other set of AAs is in use.

A small set of headphones for the radio will also help reduce battery drain and therefore increases the radios battery life before recharging is required.