Can you use regular knife sharpeners on damascus steel?
Yes, you can use a honing steel with a damascus-style carbon steel knife blade.  Depending on what you have, you may need to get a harder honing steel, because the carbon steel of the knife is harder than a stainless blade.  I have a honing steel from Shun that works quite well.
Do NOT use that "Anysharp" sharpener or any sharpener like it.  Such sharpeners are designed to sharpen blades by aggressively removing metal from the blade edge.  If you use one of them, you can expect to wear down the edge of your blade and use up the hard steel there in just a few years.


NOTE: Many "Damascus" blades sold commercially aren't actually Damascus-style, that is, folded carbon steel.  Instead, they are stainless or standard carbon steel with two face plates of folded steel on either side of the blade, purely for decorative purposes.  These blades have the same care instructions as any stainless or carbon blade.