my dog tries to poop too hard when going for walks

I have a 4 Year old Male Chihuahua and for a long time now when he goes outside for walks he keeps trying to poop till his anus starts to bleed little blood (He was perfectly fine at home and poops normally)

He does this everytime and we tried pulling at his leash whenever he tries to poop but that resulted in no one enjoying the walk because we're just pulling at his leash all the time.

Going on walks is already hard enough because I live in Egypt and there's stray dogs that chase me everywhere when they see my dog not to mention the small roads and how I have to pick him up 50% of the time to cross roads a 10 minute walk feels like hours because of the struggle.

We stopped going on walks daily because he injured his anus and yelped whenever he tried to poop, So I wanted to know what the solution could be in a situation like this?