May I ask why you won't be able to do it yourself? That would make a difference. For example, will you be home during the day, and able to supervise homework during the evening (like, working in your home office, or taking care of any younger children at home)? Or will you be out of the house during the school day (at work, or taking care of other responsibilities)? Or are you not able to be involved in the school process at all? Your involvement will affect what you pay a teacher.
And regarding your son's issues: are these issues documented by a doctor and therapist, with some kind of plan that a teacher would have to implement? For example, would a teacher have to follow doctor's instructions in order to help your son behave or sit or anything like that? Is there a plan for helping his learning delays and behavior issues? A teacher would need to know these issues, be able to comply with a therapist's or doctor's orders and be comfortable implementing them. Not all teachers or mothers have experience with that.
Homeschooling is usually not self-guided, for the most part. Of course, there are some types of homeschooling that are called "un-schooling", and some kinds of curriculum are more relaxed, and some children are able to function pretty independently. However, most homeschooling parents are very involved - they teach, test, tutor, encourage, support, and guide.
There are some free online public schools, where the child attends classes virtually, take tests and do their work with access to teachers and tutors. You can look online to see if these are available in your county, town, or state. Also, you can seek your doctor's help in getting your son a 504 plan if he needs that, and the online school would be able to adjust his education plan.
And even if you won't be teaching your son, you'll have to plan on meeting with the teacher periodically.
You'd have to inform any potential teacher or homeschooling mother of your son's needs, and what your requirements are, and get some hourly rate quotes.