You'd have to have modern day lifeboats on deck, modern guardrails, modern safety features, lights, fire exits, widths and dimensions of corridors, the deck, would all have to abide by modern maritime safety standards for commercial liners. Best case it would always have to be a compromise if it were to be legally sea worthy, especially commercially. Now for the logistics, I'm not sure how possible it would actually be.
They reenact civil war battles all the time to remember and educate a new generation to our history how would this be any different? Half the people here saying it would be disrespectful you know would be first in line for a ticket if given the opportunity. I think if done respectfully to educate and to teach the history of the original ship and ships of that era and used as a lesson and reminder of the tragedy then absolutely it can be done. There are many examples of similar re-builds of classic boats, buildings, cars etc from history.
I don't think a 'replica' ship would be disrespectful by default.