What's the worst that can happen when attempting to fly with double-edged razors?

The main issue is that the blades are extremely sharp and I assume that with bad intend you could do harm. Just last week I wanted to bring a cheese slicer which I had to repack as checked luggage.

I don't see the danger in a cheese slicer. The razor blades are a different thing, here I can see the risk.

Pack them as checked luggage and you are okay. If you still want to travel light, there are three options. Your blades are confiscated, you are asked to go back and check you bagage in, or you are going to be subject to additional security checks with the risk of missing your flight.

Personally, I wouldn't risk it. These blades are really cheap, so why not buy them in a drugstore at your destination?

Finally, there is a ressurection of the old barber profession, you could also choose to enjoy a good relaxing shave while you are abroad.

Any answer is opinion.
But the following seems to be in the range of possible:

The short answer is, in the worst case it could have life changing (or even ending) consequences far beyond what you'd possibly wish for or imagine. While worst case is unlikely, the current world situation could produce circumstances that make you look like you may be involved in some larger scheme. If that occurred, anything could happen.

You asked for worst case.
The "911" hijackings were (reportedly) carried out with "box cutters" - knives with an under 1 inch blade in normal form and too fragile to extend much more than that and use as a weapon. In trained hands a lethal weapon. In untrained hands a potentially lethal weapon.

A razor blade could be made into a very nasty knife indeed by mounting it on a suitable handle. It would not be as robust as a box cutter but, in trained hands it could cause immense pain instantly in a fight and also would be both a disabling and lethal weapon. (Ugh: Carotid, wrists, Achilles tendons, hamstrings ...).

At the very very very least a TSA agent should take them from you.
You asked for worst case.

If they decided to teach you a lesson they could get you to 'cool your heels' for a few hours until your plane was a distant memory. Your travel insurance may not cover this as it relates to terrorism. Or they may give you a bed for the night. They would be wholly justified in doing this under their regulations, AND in common sense. Your 10 blades could equip full hijack operation. The handles that they mount in would be unremarkable in the luggage of your accomplices. But, you asked for worst case.

In a Bangkok market I purchased a Shuriken "just for fun". I thought nothing of putting it in my check in baggage and it came home without event and is now an ornament in my home. As a weapon in my hands it is useless. To one 'trained in the art' it is lethal. Mine looks similar to this (but nicer :-).

Some months after my return a man brought in a range of weapons of similar general style from Asia. Not just Shuriken's but perhaps Nunchukkas, and other 'martial arts weapons'. From reading the court transcripts I am convinced that he had no worse intent than I did. His protestations sounded just like what I would have said. It availed him not. His toys were confiscated (of course) and he was either heavily fined or imprisoned (memory dims). I recall that the penalty was unimaginably severe for what I am sure was a completely harmless act.

If for some reason a few or even one of your fellow travellers was on the TSA watchlist as a person of interest and they put 2 + 2 together and got 7, you ending up in court would not be worst case. And, if another airliner had just been diverted by persons unknown as you went through security and if some of your "companions" were their 'friends', what chance do you think there would be of the TSA agent simply confiscating your weapons system? Finding out if waterboarding and the rendition flights have really stopped would be worst case. Hope that the destination is not Egypt, I'm told. (Really).

Likely? Of course not.
Possible? Yes !!! :-(
A very very very severe outcome is definitely a possible worst case with a degree of probability that makes it not worth risking. Put them in your checked in luggage.