As catlover2 said - please do not take both the cat and the dog out at the same time. You may be able to control one but not both in an emergency. Which one would be left behind?
If you lived in the country I would be more apt to say go for it. Normally there are lots of open areas where a kitty can explore in safety with the harness on. But you live in a populated area. Or at least I am going to assume you do seeing as you mentioned you live in an apartment.
A scenario or two -- You are outside walking your pets. Another dog comes up and petrifies both your dog and cat. Your cat reacts by slipping his harness. Your dog reacts by yelping and hiding behind you. What would you do? -- Again, walking both pets - A very loud horn blasts close by. Gizmo is scared and reacts the same way as before. Or he decides you would make a good climbing post to get away from the thing that scared him. He scratches you badly. Now you are in pain and trying to control a cat who just wants to find a place to hide and a dog who can sense something is amiss. Disaster!!
I have a cat (my feral gal Storm) who this past summer was being kept indoors because of an injury. When she was almost healed I decided to take her out for a walk on the leash. Hubby was building her outdoor enclosure but it wasn't finished yet and she was getting owly. We were walking slowly when she suddenly made a quick backward movement and slipped the harness. Easily done. Cats do it all the time. She went under the deck luckily and I was able to catch her when she came out. Hubby was watching. He later said he would not have believed a cat could slip a harness attached to two leashes as easily as she did.
The point I am trying to make is what would happen if you had Gizmo outside and he slipped his harness? It is next to impossible to catch a cat who is terrified and just wants to get away. In a populated area a lot of times that getting away would be right out into a busy roadway.