Beeswax itself does not pose any inherent kashrus problem. From the OU website:
Beeswax is a substance secreted from glands in bees’ abdomen. Bees use this wax to create the honeycombs in which they store honey. Beeswax is used in foods as a coating to fruits to extend their shelf life, to give a shine to round candies such as chocolates, jelly beans and candy corns and as the base for a flavoring, beeswax extract.
At first glance, it would appear that neither of the Gemara’s two reasons to permit honey would apply to beeswax because beeswax is a secretion of the bee and isn’t honey. However, many contemporary Poskim have ruled that it is permitted, and the primary reason given is that since beeswax is an inedible non-food item, it is viewed as being pirshah (an animal’s waste material) which isn’t subject to the issur of yotzeh min hatamei. This position is supported by many ancillary proofs from earlier Poskim that beeswax is in fact kosher. One of those proofs is Magen Avraham 321:16 who rules that one should use beeswax candles for bedikas chametz rather than animal fat candles, so as to guarantee that no non-kosher fat drips onto one’s dishes. The Magen Avraham implies that drippings from a beeswax candle pose no kashrus concern.
Thus, it is generally accepted that beeswax is in fact kosher.
From the Star-K website:
Used to form the honeycomb in the hive, beeswax is secreted from wax glands located on the underside of the abdomen. Bees grow from larvae into mature bees in the cells of the honeycomb. They also store various other products besides honey.
In its original state, beeswax is used in non-food grade applications since the human body cannot adequately digest this material. It is commonly used in candles, lipstick, shoe and floor polish, as well as buffing wax for surfboards. Since it is not a "ma'achal," a food, its status as a yotzei min hatamei (an actual product that is secreted from the bees) does not make it non-kosher (See Igros Moshe, Y.D. 2:24 – V’gam. See also Mishna Brura 158:14). Therefore, beeswax is considered kosher provided that no non-kosher solvents are used in its processing, and it contains no non-kosher additives.... It is even permissible for one to chew beeswax for its pollen content, or even to swallow it, with or without the honey mixed in.