The wolf would be moving around in a quiet manner and paying a little bit of attention to the things around. It would not be hunting, and it would not be absentmindedly walking without purpose. "Slinking" is a funny word. It sort of has the same meaning as "sneaking around", like how an animal will sneak around looking for food. But slinking is something that has a little bit of a shameful feeling. A slinking animal isn't looking for anything, it just wants to move around without being noticed by anyone. You can use this word with people too. "He slinked away in shame" means that he must have done something embarrassing so now he's walking away and wishing everyone would stop looking at him.

An article is needed. A/The wolf was ... back and forth. ... pacing back and forth is very natural. (pacing is associated with back and forth) without "back and forth," other verb choices are walking, approaching, and leaving. Adverb choices are quietly, silently, furtively, and stealthily. Slinking away is possible [=leaving furtively]. Slinking back and forth is not possible.