I am not vegan, but was wondering whether vegans will use bee's wax.
My guess is that, given most won't eat honey, the answer is no but the method of collecting wax can be different, for example it could be taken from abandoned hives.
In general vegans avoid all animal products. Beeswax, used in some cleaning products and cosmetics, is not permitted in products labelled vegan, for example by the UK Vegan Society (and, to the best of my knowledge, its sister organisations around the world).
Of course, a person who considers themselves vegan may choose to compromise in some circumstances, or may consider it unobjectionable in a particular circumstance to use an animal product. As you mention, there may be a way of collecting beeswax that apparently causes no harm and might be considered eco-friendly, and some vegans may decide to use a product that contains it.
However, one aspect of the ethical theory behind veganism for some, is the idea that we should not use animals in any way. Veganism means avoiding complicity in such use if possible. Therefore, if bees have been deliberately kept, then using the beeswax even from a hive they have abandoned, could be considered complicity in the use of animals.
So, it is perhaps an edge case, but since circumstances of production are hard to monitor, and folks' philosophies may differ, typical labelling guidance from vegan organisations at least, considers beeswax not vegan.
Soya wax is a commonly used alternative.