Sounds like the "principle of the thing" is more important than the "actual thing" in this case.
Wearing the shoes to the shop
Claiming not to have any other shoes.
Not being satisfied with them being sent off.
Being satisfied with them being sent off but not with a standard 2 week turnaround.
It was daft wearing them into the shop - you wouldn't do that with defective trousers or any other item of clothing. Even a hat.
I don't believe you don't have any other shoes.
You probably won't want the same boots back so send them off and get a refund and in the meantime buy other boots then you can carry on as per usual.
I'm sympathetic that your shoes wore out too quickly, but you sure don't make it easy for yourself.
Plus 1 to this.
I'd be being pretentious if I claimed I'd never taken a similar attitude; I certainly have. But nonetheless it's not the right attitude. The only one you're actually hurting is yourself.