First before taking a rat outdoors, please read my thread on the subject.... It is a dangerous thing to do, but with the right rat and the right person and proper training and testing it's very doable.
This is a spot in our safe site, which is a 40 acre park surrounded on 3 sides with water. My daughter loves to climb trees so they aren't a problem. Fuzzy Rat a great true shoulder rat is on the ground exploring and Amelia who was not cut out to be a true shoulder rat is hiding in the tree. Even a rat that can't be a true shoulder rat can come to a place like this, where she can't get hurt or lost.
This is Max passing her true shoulder rat final test. She earned her place here and proved herself confident and competent... You don't start here, you work up to this.
And yes, this was taken in a large crowd under the town fireworks display. Fuzzy Rat actually liked fireworks, while Max can handle them without panicking... But if fireworks at night in a crowd isn't going to panic a rat... your pretty safe with her elsewhere.
And Max doing a meet and greet afterwards...
And just for fun, Fuzzy Rat exploring on her own at the beach...
It can be done with the right rat, but it is never safe, it's risk management...
Now as to leashes and harnesses, I'm generally against them. Rats are expert escape artists and they can literally squish themselves into and out of almost anything. Thinking your rat is safe because you put a harness on her is a terrible idea because you are outdoors with a rat that hasn't been trained or tested that most likely can panic and escape... It's not the harness that get's your rat lost or killed, it's the false sense of confidence it can inspire.
If you are really interested in training a true shoulder rat start out at a safe site before you get the wrong rat lost or killed. With the perfect rat like Fuzzy Rat, it's actually pretty easy, with certain other rats it takes a lot more work and with a normal rat you'll find out it just isn't safely doable. No matter how long we worked with Amelia as soon as we put her down and stepped away from her she panicked and ran for cover... we couldn't even put her down to go to the bathroom outdoors. She was almost two years old before she could even come down from her tree at the safe site and forage around under the branches. By the time Fuzzy Rat was only 4 weeks old, she had already escaped, explored on her own and come back when recalled after nearly an hour... which is when I moved all rat training to the safe site. Fuzzy Rat was a brilliant escape artist, she was also incredibly competent at taking care of herself and avoiding dangers and she always came back to us or back to the house or car on her own. Max and Cloud need more supervision. And as soon as Max figures out where the car is she's on her way there. Cloud basically hangs out with us, which is nice too, she'll explore, but keep us withing visual range which makes her pretty easy to handle.... No true shoulder rat can panic, if your rat panics when outdoors, that's pretty much the end of her training, you won't get her back and you will lose her or she will dart off into traffic and get killed. The rest comes down to your skills and experience and how well you train your rats.
This isn't an activity for everyone, consider your risks carefully before going beyond the safe site.
Best luck.