There are plenty of substances that, if correctly administered intravenously, will kill somebody. The problem I think you're going to run into here is the scenario you've set up. To bump into somebody and accomplish an injection, the assassin isn't going to manage an IV injection; getting a needle into a vein takes time and skill, as well as a degree of cooperation from the person receiving the injection. That means whatever the assassin is doing is more likely to penetrate a layer of skin (either an intradermal or subcutaneous injection) or the muscle (an intramuscular injection). The body processes everything that goes into skin, fat or muscle slower than it does when it's injected directly into the bloodstream.
Your 2-3 minute window then becomes an issue. Insulin OD can take up to an hour to cause a coma in a healthy person, much less death. The high-end barbiturates, tranqs, and narcotics will also not act within that time frame if injected SQ, ID, or IM, and the amount of any of those you would need to kill a person is highly variable, making them a poor choice. Potassium Chloride is what is used for lethal injection, but again, it's used IV. It stops the heart.
Botulinum neurotoxin is the most poisonous substance known. But even it has to be administered in a specific method to cause death. By injection it treats over 50 pathological conditions. If inhaled, 0.001 mg of it is fatal.
My suggestion would be to not worry about the specific chemical in the assassin's device, but rather focus on the suspense of the scene and its administration. Or give the chemical a nickname and say something like it's "a lethal blend of favorites." If the scene is scary or adventurous enough to enthrall your reader, they won't be worried about just what was in that needle.
Best of luck,
Tux