I have an idea about this, but it rather depends on it being made by Koch and having a product code on the back. So can you see a product code? I have a similar thing (not the weather station) we picked up in Germany and if I recall had a similar problem. I think the German version of the instructions on their website were more helpful in this respect. But you can only search by product code.
The website was
www.koch-thermometer.eu if you want to look yourself. I may be in a position to look through the German and provide you with a clue if necessary, if you locate it.
However, having now seen just how many different manufacturers make such gadgets - I'm probably wrong. However the essence of it is that no-one would limit their possible market by not allowing for other than one time zone. In the case of the one I have, during time setting, the last possible adjustment is a 2 digit number which is hours offset from current German time. Up and Down were used to adjust this in the same way as all the other time settings. So, might be worth looking for. I realise that this doesn't actually disable it, but would presumably be just as useful.