I'm a bit confused. I assume that you're only going to be posting cassette tapes (rather than the actual 'Walkman') whenever you send an audio letter, so you need to ensure that you've got some equipment which can record a tape and that your aunt has got a 'Walkman' to play it. I'll assume, for the moment, that you've already got something to record the tapes on and that you just require something for your aunt to play the tapes with:
It would be nice if your aunt could use the 'Walkman' for something else in between receiving your audio letters, so I suggest getting one which incorporates a radio. Argos have several on page 908 of their current catalogue. Elderly people, with restricted vision, can sometimes find 'in-ear' earphones a bit fiddly but the Panasonic RQV77 (Argos Cat. No. 512/3353) comes with some nice solid headphones, which might be better. It incorporates an AM/FM(Stereo) radio and costs �17.99. (Don't forget to buy some AA batteries as well).
As I've stated, that option will only work if you've got something to record the tapes with. If not, you'll either need to buy something like the Sony TCM939 cassette recorder (Argos Cat. No. 510/1849, �24.99) or look for a cheap (secondhand?) 'boom box' which incorporates a microphone.
My only slight concern about this arrangement is that it doesn't allow your aunt to reply in the same manner. If her eyesight is failing, she might feel rather frustrated if she can't record letters to you (rather than writing them). Although it would mean losing the radio option, it might be better to buy her the Sony cassette recorder.
Chris