The plastic tikka stock has a lot of fine scratches on it which look like fine white marks against the dark grey of the stock. What can I do to make all of those fine scratches disappear or at least fade a bit?

I am not sure it would work on your Tikka stock, but CLP on issue, worn, AR15/16 stocks will darken them a bit and cover up surface flaws. Might give it a try, can't hurt anything.