Battery to replace by adapter
7.4V is probably a 2 cell lithium battery, and the voltage from those can actually be over 8V when fully charged.  

7.5V is a common setting on adjustable power supplies and being close to the sticker voltage and within the normal voltage range of the battery should be ideal.

Assuming it's a radio receiver only (not a transmitter) it's power
requirements will be reasonably constant so it can be assumed that it wants about 333mA (1000mAh divided by 3 hours)

So a 7.5V DC supply of more than 333mA should be sufficient, I'd go for 500mA or more, to allow the volume to be turned up a bit if needed. too much mA capacity will not cause problems (not until ridiculous levels where the cable becomes too heavy etc).