The key to this is to be convincing. True, having no actual secrets to use for weapons does make the process more tricky but it can be done. In order to create convincing blackmail, it is key to have both the right materials, methods and, of course, motive.
Firstly, the correct materials. Do not be fooled by TV shows, using cutouts from magazines does not make your blackmail any more sinister. The best thing to use is a plain typing font. This will not only make your message easy to read but it will protect your anonymity as there is no way to trace it. It wil also keep you from getting covered in sticky glue and save you the trouble of cleaning up any potential evidence that could be used against you. Keep the paper plain and be sure to use black ink. Make sure it looks as impersonal as possible so no-one can trace it back to you. If you wish, you may include a creepy last sentance to freak your victim out. Some good examples include: "I know where you live..." and "Watch your back."
Methods are also a highly important part of any blackmailing attempt. Make sure you have a wide variety of messengers available to drop the letters through your victim's door. This will prevent anyone from spotting a single person acting suspiciously and, if the occasion arises, you will be safe to drop the letter off yourself. Make sure your messengers dress as normally as possible, no scary black trenchcoats and dark glasses. This will simply draw attention to your mission and may lead to your plot being uncovered. With no secrets to protect yourself with, you would be very dead, very fast. Keep a certain air of mystery about what you're doing and, if desired, leave a calling card. Pressed flowers and other small objects are best for this as they are small and not particularly out of the ordinary. However, when using calling cards insure not to leave any fingerprints on them.
Finally, and most importantly, make sure you have a good motive for your blackmail. In normal circumstances, you would use the secret or secrets you had unearthed to make your victim comply. With no secrets, insure you at least allude to the fact that you could leave a dark smudge on their reputation and subtly hint at nasty consequences or "accidents" that may occur if your victim fails to comply. Keep everything as vague as possible, let your victim's imagination do your dirty work. Even if you yourself don't know any secrets, there may be some darker memories or actions your victim would prefer to forget. They will no doubt spring to the surface when your letters are recieved. Once you have your victim hooked, keep up the pretence that you know things until they give in.
When you have what you want, simply stop sending letters and enjoy your reward.
Final note: Lie. It works.