Cutting out at part throttle

[stryped]

I have a 1996 Silverado. Only code is cat below threshold and has been there for awhile. I replaced the fuel pump recently but it did not cure my problem.

 

The problem is at part throttle, barely giving it any throttle, it cuts out. Bucks and things. It seems worse when cold. At WOT no problem. Even going up hills no problem. Actually, seems worse going on a flat highway. Accelerating no problem. Idle no problem.

 

Is this safe to drive and what could it be? In APril, I replaced the spark plugs/cap/rotor. Ignition module went bad at that time and I replaced it. All with autozone parts. (I know not the best, but only thing available to me at the time. Like I said fuel pump is new. Fuel filter is new.

 

Please help me!

[stryped]

One more thing. This part throttle cut out only happens while driving, never while parked reving it.