If you think you are missing one, in most cases I would guarantee that you are actually missing the M60E4 which only appears once in the game.
Right at the end of 'Game Over' when you are defending yourself on the collapsed bridge, the very first enemy truck will pull up, ram a parked car and reverse.
An enemy soldier jumps out of the front passenger door and is armed with the M60. Kill him, pick it up and get a kill with it and that should be the last gun you need in the game. No resets or save deletions required.
I have provided a full comprehensive list of all weapons needed below.
I do not believe that C4, Claymores or Flashbangs are required as these did not increase my progress bar or were never used to kill an enemy. I'm also not 100% sure about grenade launchers but if they are required, you do not need both the M203 and GP-25 as once again my progress bar did not increase after a GP-25 kill but I hadn't started checking until way after my first M203 kill.
I'm also not sure regarding different versions of the same weapon i.e. MP5 and MP5SD and M4 and M4 Special Operations Modified but would recommend using all variants.
Pistols
Beretta M9
HK USP.45 (also has silenced variant)
Colt M1911
IMI Desert Eagle
Submachine Guns
HK MP5 (also has silenced variant)
FN P90 (also has silenced variant)
CZUB Skorpion
Izhmash AK-74U
IMI Mini-Uzi
Assault Rifles
Izhmash AK-47
HK G3
HK G36C
Colt M16A4
Colt M4A1 (also has SOPMOD variant)
Shotguns
Winchester 1200
Benelli M1014
Light Machine Guns
FN M249
Degtyarev RPD
USO M60E4
Sniper Rifles
Remington 700
Izhmash Dragunov SVD
Springfield M21 (also has silenced variant)
Barrett M107 (static weapon used only in 'One Shot One Kill', not sure if required)
Launchers
Raytheon Javelin
GD Stinger
Bazalt RPG-7
Equipment
M67 Frag Grenade
M203/GP-25 Underslung Grenade Launcher