That should work really well. Your radio most likely puts out 3.6 to 4.5 V (from the three AA batteries). You will want to check it with a volt meter, but most likely the tip if the 3.5mm plug will be positive and the sleeve will be negative.
Here's the wiki page for the USB remote :
USB RemoteYou should be able to adapt this drawing from there pretty easily - just delete the switch and wire your radio up in place of the CR2032 Lithium battery :
