I am not no expert, but if the old links that are 404ing have genuinely no new destination then it is better to ignore them then it is to redirect them. Over time as google crawls the site they will disappear. You are not down ranked in any way for this. For a new site this may take some time.
Have the same problem. The old 404 not found links don’t disappear about one year. I was hacked with Japanese Keyword Hack thru one plugin which have backdoor. I make my website from new and links still showing in webmaster after one year, sad.