I don’t know if this is working as intended, but I have Throw Grenade bound to the C Key, and whenever I throw a grenade while standing over a dropped weapon I will pick it up. I imagine this is a carry-over from the original Combat Evolved port where there was a dedicated Swap Weapon keybind, but MCC does not provide an option to un/rebind it, even if you are using that key for another function.
I have tested and rebound throw grenade to another key, which solves the issue, and C still functions as Swap Weapon, though I would really prefer not having to change my grenade key.