In some states and countries, only parents and "official" caretakers like schools are allowed to spank. Parents cannot "delegate" that authority to anyone else. Heck, in some countries even parents can't spank.

As for sexual abuse, if he either feels abused or jokes about it, stop. Find some other way to discipline him. Assuming he genuinely cares about spending time with you and isn't just using you, separation from you is usually effective. Say "when you misbehave, I cannot be around you. The next time you misbehave, I am sending you home." Then do it. The next day tell him it's a new day and he gets a fresh start.

It will take a few times, but in almost all cases where he genuinely values your company, it will work. It may not work as well on kids that are in double-digits though. But then again, neither does getting spanked.

I would also recommend that you do not spend time alone with this child. The fact that he's joking about sexual abuse means someone could misinterpret that joke and ruin your life. Always have another adult around, for your own protection.