The only thing I can wear is my shoes.
Can I use shoes as a collective noun in singular, as in the example?
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Your example is fine as written. Imagine the following exchange:
You have lots of clothes you can wear to the party, right?
No, the only thing I can wear is my shoes.
In your example, the singular verb "is" agrees with the singular subject "the only thing..." (the verb agrees with the subject, not the complement).
The complement "my shoes" is plural (not a collective noun) - so if we were to flip the order, it would be:
My shoes are the only thing I can wear.
If we want to use a collective noun, we could write:
The only thing I can wear is my pair of shoes.
("Pair" is the collective noun.)