Your plan literally puts you in the music business -- so you're smart to want "to do this right." You will need a number of agreements: (1) a license from the owner of the musical composition copyright for the song [i.e., the song's publisher], (2) a license from the owner of the sound recording of the karaoke version of the song [i.e., the music label that created the karaoke recording], (3) a work for hire agreement with the singer you will hire to record the song and any producer or other recording personnel, (4) a bill of sale for when you sell the song, and (5) any others that your own Florida-licensed entertainment attorney thinks is necessary. There are good entertainment attorneys in Miami so track one down and discuss your plans. Step one, in my book, is for you to create a company from which you will do business. Then work on acquiring these agreements. Before taking step one, however, you should read at least one book on how do business in the music business [visit the link below]. Good luck.
The above response is general information ONLY and is not legal advice, does not form an attorney-client relationship, and should NOT be relied upon to take or refrain from taking any action. I am not your attorney. You should seek the advice of competent counsel before taking any action related to your inquiry.
Find an entertainment lawyer to do the multiple licenses you need, to clear your versions, and too protect your versions against copying.
I am not your lawyer and you are not my client. Free advice here is without recourse and any reliance thereupon is at your sole risk. This is done without compensation as a free public service. I am licensed in IL, MO, TX and I am a Reg. Pat. Atty. so advice in any other jurisdiction is strictly general advice and should be confirmed with an attorney licensed in that jurisdiction.
You cannot do this legally without certain licenses. You are creating a derivative work, rather than a cover. This is important because if you were creating a cover, you would be entitled to a compulsory license. However, because you are changing the words and creating a derivative work, you are not entitled to a compulsory licenses (which costs 9.1 cents per unit). Instead, you will need to negotiate a mechanical license to use the composition and create the derivative work. You will need to obtain this license from the owner or administrator of the copyright in the song---either the original songwriters or or their music publisher. Be careful because if there is more than one songwriter, you may need licenses from more than one music publisher. Further, in addition to the mechanical license to record an audio version of the song, you will need a synchronization license from the same publishers or songwriters because you want to use the song with a photo montage or on a video.
Furthermore, you are also proposing to use a karaoke music track over which you will record the song. If you use the karaoke track, you will need to obtain a license from the owner of the copyright in the sound recording (the karaoke track). This is ordinarily a record label but in the world of karaoke it may be a karaoke company.
If you record the song on your own with original musicians, you will not need the license for the karaoke sound recording (since you are not using it). But you will need releases and/or artist agreements from all musicians who appear on your recording (because they own copyrights in their performances and you need the right to use those performances). And you need a license from whomever physically makes the sound recording (whether a producer in a studio or your friend on an I Phone). Whoever makes the sound recording owns the copyright in it unless they enter into an agreement pursuant to which it is provided to you as a work for hire or assigned to you.
As you can see, this gets quite complex. Thus, if you want to pursue this business, I strongly advise you to retain IP/music licensing counsel (I do this every day). These license agreements get very complex. Further, it is not always easy to track down the songwriters and publishers and then to convince them to let you use their song in your project. You will be surprised how often they turn you down even if you offer to pay them a royalty. You need a lawyer who knows how to speak the language of these people and can get in the door---they probably will ignore you if you try to handle this on your own