This isn’t quite “black market,” not unless you have someone doing work that requires licenses and permits and you are trying to duck all of that.
By “pay in cash,” you mean you have to pay in greenbacks, instead of by check, in order to directly cooperate with a deceit? Or do you mean that you will be paying him like an independent contractor in the knowledge that he probably will not report his earnings as he ought to do?
Filling out his tax forms, paying quarterly taxes, and reporting one-time income as required by the welfare authorities is not your duty, provided you don’t directly encourage him to violate the law. Refusing to pay him in a way you’d never pay a total stranger in order to help him in a deception is your duty. Do not try to play stupid, as if you always pay debts of over $1,000 in cash when you actually never do and never would, except that you are being asked to help someone else evade the law. If your parents want to pay this guy, it is not your business to worry about how they pay him. You ought to be clear that you’ll have nothing to do with running a scam on the government.
A contractor is licensed and bonded
in order to protect the customer. Since you are renting, look at your rental agreement to find out if you are required to use licensed and bonded contractors. If you are, then follow the contract. If not, ask your dad who gets to pay if this guy messes up the job or sets the building on fire and the apartment owner sues you for damages and breach of contract. What if the man hurts himself and sues for damages? How is that covered? If you are not too old, your parents may be able to include your apartment on their homeowner’s policy, BTW, which could save you a ton and make high coverage attainable. With the home policy, too, you need to know what is and is not covered before you invite anybody in. Line up your insurance before you line up your movers!!
Also, if you are paying for this work yourself, you need to have a contract specifying what is to be done and what you are expected to pay. What happens if the work is not done correctly? What if it is not done on time? What if the place is torn up and then nothing is done after that? What if he does something he claims you asked for that you did not authorize? (The contract ought to require change orders be in writing.)
If you have nothing on paper, you could wind up in small-claims court or even a higher civil court when the work is done and his memory about your agreement is different than yours. I do not know how many attorneys I have heard say that most stupid lawsuits could have been avoided if just one party had insisted on a simple industry-standard contract before the work started. This is why no one in his right mind runs a business without a standard work contract. Lawsuits are a stupid waste of money, and usually avoidable.
Protecting yourself from lawsuits, BTW, is an important part of protecting your credit history. Don’t neglect it. Get on the renter’s section of your state and city web sites. The chances are that your tax dollars are paying for someone to answer these questions that people without the means to go to an attorney have: that is, when do you need a permit to get work done on a residence, what work may only legally be done by a licensed contractor, and so on…