I have noticed that the LATW (Light Anti-Tank Weapons); BAZ (Bazooka) and PSK (Panzershrek) have a zero range on the back of their counters. This would infer that the LAWT's can be used in CC
Your inference is mistaken. They have a number for rolling TH at range 0 because sometimes the range to your target will be 0 hexes, i.e., the vehicle is in your hex!
No SW (of any type) can be used in CC [EXC: in full ASL, German MMC can sometimes use ATMM, and occasionally you'll see special rules for British squads making use of Gammon bombs].