Removing wires from old breaker
Breakers are meant to be replaced.  Once it is pulled free from the rails inside the box there should be no electric power on those wires.  But it sounds like the box itself will still be live.

If there are no screws then most likely you will find a small slot right next to where the wires are pushed into the breaker.  Use a small screwdriver in there to push the internal retainer clip back to release the wires.  The wires themselves are probably cut and stripped correctly already.

Once the wires are inserted into the new breaker it should just click into place inside the panel.  

btw, there definitely is a main breaker somewhere.  Usually the fire department will want to be able to cut off all power before they begin to spray water inside, so it is supposed to be in a location they can find quickly in an emergency.  

If your incoming service is underground then the main breaker might be in a box at the sidewalk, in which case you may not have access to it - sometimes the boxes are green with a key-lock on them, and often they serve as main feeds to more than one home.

When working near the live rails, remember the electrician's left-hand rule:  Keep your left hand behind your back.   That way if there is an accidental discharge it will go through a limb and not through your heart.

If you have successfully gotten the breaker out without touching the rails then you should have no trouble getting the new one back in after the wires are transferred over.

--Edited based on your comment