Did the smaller camps focus on torture?

No, it wouldn't be accurate. There is a wall in Washington D.C. that lists the name of every soldier who died in Vietnam. Where's the wall of every holocaust victim that was tortured and killed in WWII? Lots of names of survivors tho. All with a story to tell.

My best answer would be it depended a lot on who was in charge of the camp. Himmler would assign the commanders, he obviously would assign sociopaths who would get the job done.. especially in the 6 major extermination camps. For example, the commander of Auschwitz expressly forbade torture, he just wanted to trick the victims into the underground dressing rooms. From there the guards would usher them into the next room, the guards had guns and night sticks so the victims wouldn't fight back much.
One very sad thing I read recently was when the Auschwitz commander gave the order to murder 40,000 women in just 2 or 3 days. There were about 50 trucks, with approx 80 women in each..they'd be dumped off right next to the huge gas chamber/crematoriums(named Auschwitz 1, Auschwitz 2, etc). The women were already so weak and delirious from massive malnutrition, fatigue, disease they simply walked or crawled the few steps down to the dressing room and a few minutes later they were gassed and shortly after cremated. Their ashes dumped in a nearby river.

It depends on the camp. Mauthausen, where my father's family was sent, started focusing on granite mining and the torture was a part of the process to keep the prisoners under control. My mother's family was put in the Ghetto in Vienna and eventually sent off to Aushwitz for the final solution.

Torture was used moreso to keep prisoners under control. This is why the Russian and N. Koreans followed in suit with their prisoners.