Einsteinian Physics Fail.
If you actually could travel at the speed of light and throw a peanut straight in front of you, such that it actually was surpassing the speed of light, which it can't, it would travel back in time and hit the other spaceship before you even decided to throw the peanut, thereby breaking causality.
...then drop a peanut out the airlock...
No throwing involved. And really, even if you're only travelling at point nine cee, you're getting more than four-fifths the energy of the peanut half of a peanut-antipeanut explosion. The only problem is that when you go much slower than light speed, your enemy gets the chance to DETECT you and raise shields...and that's not something you want.
And Beorn, I don't know of many sci-fi series that actually claim to break the speed barrier. Mostly they warp space, including Star Trek and I think also Star Wars, so "there" is right next to "here" and then they just trundle across before unwarping it. Makes it a lot easier to stop that's for sure! Getting up to near light speed with impulse drive is actually way harder than going to warp in many settings, and often requires less energy with whatever exotic stuff they have.
There's a problem with throwing ANYTHING out of the airlock at lightspeed. By the time you push the button to open the airlock, you will have overshot the target by several thousand parsecs because of relativistic time compression.
So you drop the peanut at a light-minute out SUBJECTIVE.
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God knows how far out you are, but surely you can do something like that.