Olden version of "psychopath"

Solution 1:

As user121863 said, in the 1850s the general understanding of mental disorders lacked nuance. So there weren't many "posh words", as you put it, and Hot Licks has them covered.

The following are synonyms for 'mad person'. I'm not sure if they would all be deemed slang:

hatchet-man from 1876
nasty man 1863-
cutter 1568–1734
frantic (noun!) 1574-1758
crack-brain c1570-1831
madbrain c1570-1616 + 1876
shatter-brain 1719 -
maniac 1763 -
dement 1857 -

berserker: The adjective 'berserk' is still used to mean crazy, but according to Etymonline, the noun 'berserker' (from the Old Norse 'berserkr', meaning "raging warrior of superhuman strength") is the oldest form of the word in its revival in Modern English (1822). 'Berserk' appeared some twenty years later.

And perhaps your readers would believe these killers, from Old English) were still on the loose in Birmingham in the 1850s:

bane (from 'bana')
slaga - hence faederslaga (father-slayer)
queller (from 'cwellere') - hence boyqueller (boy-killer), which was even used in 1606!
morþ (morth)