They are not looking for it because it is a good weapon against aliens or because they can't make another one. They are looking for it because it is a murder weapon, as in, a weapon which was used to commit a murder. Anybody analyzing the weapon would find alien blood/ DNA on the weapon. Thus proving without a shadow of doubt that aliens exist and there is a conspiracy to keep their existence secret. In fact, not only do they exist but "we" (as in, some human beings) specifically designed weapons to kill them!
An analogy is in order.
Let's say a person X committed a murder with a modified ice pick then ran away with that same ice pick. The murder weapon is missing. Police is looking for murderer and they find X but X got rid of the murder weapon. Now, police can go to court and say:
"X used a sharp object like an ice pick, only it appears to be modified in some way, there are witnesses that say they saw person looking like X at the place of the crime, X doesn't have an alibi."
That's all fine and good, but until you find that modified ice pick, all you have is circumstantial evidence. Find the murder weapon, with victim's blood on it and X's fingerprints on the weapon and police will have much stronger case.
That is what conspiracy is trying to prevent. Everybody believes that Mulder is slightly loony and conspiracy theorist. But if he finds evidence, then suddenly conspiracy is broken and people will have to start trusting him.