–zhe (著) is an imperfective marker derived from the VR compound. It often indicates a resultative state. For instance, 他穿著皮鞋 (t¯a chu¯an-zhe p´ı -xi´e/ He wears leather shoes.) emphasize the state resulting from the action.
On the other hand, -zai (在) is a progressive marker emphasizing an on-going event. In the sentence 他在穿皮鞋t (¯a z`ai chu¯an p´ı -xi´e/ He is putting on leather shoes.), progressive marker –zai (在) underlines the on-going action of putting on the shoes.
Moreover, –zhe (著) also occur in subordinate clauses to give the background of a situation. For example, in the sentence 他穿著皮鞋跳舞 (t¯a chu¯an-zhe p´ı -xi´e ti`ao -w˘/ He danced when he was wearing leather shoes.), the major event is “dancing,” while the event “putting on the shoes” is backgrounded and viewed as an ongoing state with the imperfective –zhe (著).
However, it is ungrammatical to use–zai (在) in the sentence *他在穿皮鞋跳舞 ( t¯a z`ai chu¯an p´ı -xi´e ti`ao-w˘u). Since it is impossible for someone to engage in dancing, while another activity like putting on the shoes is in progress
Reference: Chinese: a linguistic introduction by Chao Fen Sun