All perfect praise be to Allaah, the Lord of the worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and Messenger.
If something was stolen or usurped from someone and he found it with the one who stole it or someone else, then he has the right to take it back if he does not fear a greater evil than that of losing it, such as the attribution of betrayal and theft to him. It is not stipulated to refer that matter to a judge.
If one is not able to take his exact property and only takes part of the property of the one who usurped him, he is allowed to take it until he takes back his right from him in full.
Al-Bukhari said:
"Chapter of the retaliation of the oppressed person if he finds the property of the one who oppressed him. Ibn Seereen said: "He should retaliate," and he recited the saying of Allaah Almighty (which means): {And if you punish [an enemy, O believers], punish with an equivalent of that with which you were harmed.} [Quran 16: 12]"
Al-Haafith Ibn Hajar said:
"Does this means that he should take from him something that is equivalent to his property, even without a ruling issued by a judge? This is the issue known as ath-thafr (recovery of a stolen item of property). The compiler is inclined to adopt this opinion. Therefore, he quoted the report of Ibn Seereen, following his habit of overweighing opinions based on reports."
Accordingly, if you are certain that the shoes that you have found with that man are yours based on signs that indicate so, then there is nothing wrong with taking his shoes, considering them part of the right he owes you.
Allaah Knows best.