It's hard to say from the photos posted but I'd guess rosewood. I'd start off by giving mineral oil a shot easiest place to get it is buy a bottle of baby oil, you could also try olive oil. Put some on a lint free cloth (or kitchen roll) and wipe it onto the handle, leave for about 15 to 20 minutes and wipe off any excess with a clean lint free cloth.
It's hard to say from the photos posted but I'd guess rosewood. I'd start off by giving mineral oil a shot easiest place to get it is buy a bottle of baby oil, you could also try olive oil. Put some on a lint free cloth (or kitchen roll) and wipe it onto the handle, leave for about 15 to 20 minutes and wipe off any excess with a clean lint free cloth.