A cat without claws will have a very difficult time to climb a fence. They could....possibly...jump the fence though.

I have two cats....one with claws, one without. They are allowed in the fenced backyard only on a harness and when chaperoned. The harness and leash allows me to pull them out when they get into ackward places (bushes for example.) I also have bells on the harnesses to help me find them when they wander the yard.

Sometimes they whine to go out when I can't or don't want to do so. They have rather short attention span though and get over it quickly.