The mouse is most likely not made out of a one-piece mould. How would they then be able to insert the electronics afterwards? Or do you believe they put the plastic around it afterwards? In other words, it should be possible to disassemble the mouse.
Searching for how to open a computer mouse revealed a few procedures, basically like the following:
- Disconnect the mouse, and flip it over
- After removing the slider pads, unscrew the screws hidden underneath slider pads
- Separate the base and top shell of the mouse, hopefully revealing the button faces
- If you don't see the button faces, you might need to unscrew some more and do more disassembling. Take care remembering what you did to disassemble it, so you are able to put it back together again
Then you need to clean the sticky surfaces. Clean the button faces using a mild detergent, and rinse off with some water. Be careful not get water inside the electronics if possible. Continue with cleaning the top shelf holding the actual buttons/fingers. Dry it of manually, and leave for some hours so as to make sure it is really dry.
Reassemble the mouse, possibly using a little glue to get the slider pads to hold in place again. Hopefully there should now be no more tacky buttons.
Disclaimer: Opening up the mouse, will most likely void any warranty, if any.