It can be done - I've done it. it is, however, a total pain in the bum.
You have to crack the glued joint all the way around the handset, which is difficult to do without damaging the plastic. I used a table knife, and lots of patience. Eventually it will come apart, with 2 "hinges" at the top. Should be easy to fix once inside, and you can re-glue the handset when you've done - again aesthetics are the real problem, and it will take a bit of patience and finesse to get a cosmetically acceptable result. I put some sticky tape round the handset to hold it together while the glue dried.
As you rightly say, the handsets are interchangeable between 1600/2400/2500 Beocoms, so if all else fails buy a 1600 as a donor because it *should* be cheaper, but a lot depends on colour also.
Good luck.