Yes, it is perfectly fine and expresses the exact same thing. The pronoun οποίος/οποία/οποίο is used instead of που all the time, especially when there is need to clarify which noun is replaced (not the case here).
Greeks use the same word for "he" and "this". But they don't leave it out when they mean "this". There's a grammatical difference in English, but no practical difference in expressions such as this one.