Now we store several of these plastic sharpeners with our Hanukkah decorations. They like to save the colorful wax shavings in a plastic bag until the end of the holiday. The plastic sharpener look likes a large crayon, and can be purchased at most places that sell crayons and other school supplies. The shavings collect in the base. The top is removable, so that the shavings can be dumped out.
Some sharpeners come with two different size tops to use with different size crayons.
Please let me know if this hint works for you. In desperation, I even used a metal skewer and screwdriver. It still bears the scratches from my attempts to clean it. One Hanukkah, I tried rinsing the hanukkiyah in hot water, as this worked well with my Shabbat candlesticks. But there was too much wax on my hanukkiyah for this method to be very successful.