The SKS has a free floating firing pin. That safety blocks the trigger, as you'd written.
SKS rifles can double (or more with a full magazine) if the firing pin is sticking. Even releasing the bolt can result in a discharge.
That's why it is recommended loading one round initially. If that round doesn't fire when the bolt is released, then eject that one round (or fire it) and load two rounds. Pull the trigger and ONE round should fire. If both rounds discharge...well, that's doubling.
This rifle design is quite old...and it's a communist block design. The SKS is a robust rifle, but safety was not the primary concern of the design and manufacture. Be aware of that and learn the limitations of this rifle.
I had an SKS double once. Scared the bejeesus out of me! I like mine, but I'll never load an SKS in my house or keep one loaded in the house.