Firstly, the international Radio Regulations have requirements for secrecy of communication which is why the only transmissions that may be listened to legally are broadcast radio, amateurs, the standard time and frequency service, and in any case where a distress message is received.
Secondly, you may think it doesn't transmit, BUT.......
Being what is called a 'superhet' receiver, it has an oscillator in it on some other frequency, which can well be in the aircraft comms or in the VOR band. If it's CE marked, it will meet the requirements of EN55013, and the local oscillator radiation is limited to -13dBm or 50 microwatts. Doesn't sound much. does it? But a pacemaker transmitter is limited to 25 microwatts outside the body, but in practice, starting with about 1 milliwatt (about all you can reasonably get out of the battery), you get around 50 nanowatts out of the body, and they still communicate over quite a distance. Professional receivers can only radiate 2 nanowatts.
Even if it is CE marked, that doesn't necessarily mean that it meets the requirements, with CE often standing for 'Chinese Export'.
There are hearing aids with ultra low power radio transmitters in them: the power is so low that somewhere I have an email from the CAA saying they are exempt, especially as in an emergency, it is important for PAX to be able to hear crew member instructions.
Take strake's advice, although you may prefer wine, beer, whisky, brandy, vodka etc. BA have a reasonable selection, and unlike the American carriers, it is free in World Traveller and World Traveller Plus. (Free champagne is only in Club and First)