No, that's not possible.
"I'm not wearing shoes." Statement of fact. You are not wearing shoes at this moment. For instance;"i'm at the beach, i'm not wearing shoes."
"I do not wear shoes." Can be a statement of fact or it might be to indicate some habits. "I can't enter the restaurant, i don't wear shoes." or "I like feeling the grass beneath my feet, therefore i do not wear shoes."
'Am' (to be) is a helping verb in sentence where you want to say you wear something. Wearing is the main verb. So, in present simple use 'to be' as helping verb. Some past tenses use 'to have' some use 'to be'. Future tense has helping verb 'will'. Helping verbs cannot be chosen by instint. Every languge has some specific combination of using them. :)