I have an idea to patent a product that I think will sell; however, this product has electronic circuitry, which I'm not capable of producing because of my lack of electronics knowledge. Can I patent an idea and pay someone like an electronic engineer or a manufacturer to produce it and still be the patent owner?
Yes. You can be the patent owner if the invention for which you seek the patent is your idea.
If the circuitry is obvious and not an integral part of your invention, then you'd be the sole inventor. This would also entitle you to be the sole patent owner unless you produced the invention as part of your employment or you assign the patent to the company that manufactures the invention, which is an extremely common practice.
However, if the circuitry is essential to your invention and there is "inventiveness" in the circuitry itself, then the engineer who designs and builds the circuitry might be considered a co-inventor and thus a co-patent owner. This is true unless, again, the invention was produced as part of your employment or assigned to another company.
I recommend that you double-check the specifics of your intentions with a patent attorney, since the dividing line between a creative engineer and an inventor can be a fine one.
Also, before showing or discussing your invention with anyone -- regardless of whether it's an engineer or a business prospect -- have that person sign a nondisclosure agreement. Without a nondisclosure agreement or some other confidential relationship, anyone to whom you disclose the idea can use and sell your invention until you get your patent -- a process that often takes two to three years.