The only way into Qeynos currently is through Antonica, then to The Peat Bog, then through Vermin's Snye and finally The Down Below.
From the sewer entrance in Qeynos Harbor to the black market, head west to the gate. Try to make sure you know where the patrolling guards (Captain Hanstock, Oakhall and Bilur, 38 epicx3) are before you do this. There will be no guard on the left (south) side of the gate, and the guard on the right (north) can be avoided if you edge carefully. Immmediately once you get to the other side of the gate, cross over to the north side to avoid the guard past the gate on the south side of the path. Once past them, head straight and jump into the water at the first opportunity, then proceed to the fence.
To get back, follow the steps in reverse - edge past the guard by clinging to the north wall, then, just as you get to the gate but before you go through it, cross over to the south side and edge around the south wall. Once you're around the gate, head straight back to the Down Below entrance, keeping an eye out for patrolling guards of course.
Access North Qeynos through The Down Below.
Sneaking through North Qeynos is easier than through Qeynos Harbor. Follow the road north, don't get too close to the steps to the castle, and the forge isn't guarded. Once completing the mission, sneak back, teleport out, or just run to the gates and if you don't make it pay for equipment repairs.
Fighting guards isn't recommended. You are locked into combat with no ability to run away, and they ignore mercenaries.