Sheepherder put together a very nice chem pistol build, though I can't find an original post on the forum.
https://www.youtube.com/watch?v=CwaeyuuZIioBuild breakdown is in the description, just cut out the temporal manipulation stuff if you don't want it.
Not shown in the video, but with CAU armour and infused mutated dog leather tabis, you can have 100% acid resistance for using XAL, which will only cost 5 AP per shot to fire.
You will entangle yourself, but it turns you into a death machine at later levels.
Escape Artist is mandatory to use it, though, and despite you not wanting to use Psi, it is almost worth it for access to Limited Temporal Increment alone.
Cutting down Escape Artist and Cooked Shot cooldowns is painful to go without.
