Ah! I've got the same problem and well, I always carry a handkerchief. The day I don't, I really regret. I used my ties as handkerchief. I guess there ain't no cure.
Sanitisers helps me temporarily. Sometimes even a couple of hours.

The real reason I guess is nervousness, anxiety, excitation and well hot and humid environmental conditions. I know when my palms are gonna sweat, atleast a minute or two in advance.

Guess you just take handkerchief then.

My hands get sweaty too. I am giving my post graduation exams and they still sweat so much that it hinders my writing speed and I just keep on changing pens in the hope of getting a better grip on any of them so that I can finish my exam on time.

I can only suggest you a few things which I do and am planning to do as well to retain my writing speed:

1. Carry a towel napkin - you know those handkerchief sized napkins. Take one with you everytime you are planning to write an exam as this helps me wipe excess sweat off my hands and my pens as well without having to actually run to the washroom and waste my time.
2. Carry a steel water bottle - steel bottles like milton stay cool on the outside provided you are not keeping them directly under the sun. So everytime you want to just cool off your hands a little just place your palms on it for 4-5 seconds. Or you can ask for a glass of cold water from the invigilator and do the same with that. It will take some of the heat off your hands and will help you sweat a little less for a while.
3. Get a Good pen - always always and I can't stress this enough. Get a good quality pen. The pen should be smooth flowing and you should have a good grip on it because whilst writing exams even though your hands are sweating if you don't have a good grip on your pen without the sweat then you won't be able to write at all if you actually start to sweat like I do.
4. Get rubber grip for your pen - this is something new for me and I will be trying it the next time I'll be writing an exam. You know those rubber grips that some pens have, well you can get some stand alone rubber grips for either online or from the market. What you simply have to do is put that rubber grip onto your pen, yes the very same that you were planning on writing and exam with. Now once you have that rubber grip on try to write with the pen on some piece of paper and see if you will get a good grip or a good flow. This might help you retain your speed once your hands start sweating. You can also simply buy a rubber gripped pen if it has a smooth flow or take the rubber off of an old pen, whatever suits you. I hope this helps and wish you luck for your future exams. EDIT :- Rubber Grips didn't do much for me infact my fingers kept on slipping from it. Hope you have a better luck with them.