How do we practice walking outside without the pushchair?

My son will be 13 months this week and has been walking since he was 11 months but it did take a while for him to gain his balance and stop falling over every few steps. Now he walks and runs everywhere and hates being in the buggy for more than 30 mins tops, if we are stationary for longer than a few mins he will start complaining and try to climb out. I want to know when people started to go out with their toddlers without the pushchair, as I had some drama with mine recently where the strap broke while we were out and I just could not control my son! As soon as he is put down he runs off and I was constantly running after him, as well as trying to carry all of our stuff. I tried holding his hand but he kept on pulling away so he could run off and then crying when I wouldn’t let go, so I ended up carrying him whilst he struggled which made me look like a kidnapper😭. We do go to the park where he is allowed to run around but there are obviously no cars there so it’s much safer. How do we practice walking outside without risking him running into traffic or should we wait until he’s older? I was also thinking of maybe getting walking reins but not sure if those are for older children.