I am playing a lawful dwarven caveman. In Sam's Black Market I found
the Serpent's Tongue, a poisonous dagger, and an excellent weapon.
The question is; can I use it without penalty?

For Lawful characters I read in the Wiki:
|> You get a −1 alignment penalty from using poisoned weapons.
|> ("You feel like an evil coward for using a poisoned weapon.")

When I try that weapon in melee I get [in Slashem] the message:
"The twisted blade poisons the warhorse! (26 pts.)"

It looks as if there's no penalty, at least not visible from the
message. Is there an exception for Cavemen that they don't get that
penalty, or is it silently noted and I have to pay for my evil deeds
at some point later?

The source code where the "evil coward" message is created says only
if ((u.ualign.type == A_LAWFUL) && (u.ualign.record > -10))
which is a condition that would fit for my Caveman. On the other hand
there's a special artifact_hit() function defined where the "twisted
blade" message is created. - I suppose these functions are exclusive
and it is safe to use that poisoned artifact even as a Lawful. But
I'm not sure and don't want to take a risk.

Janis