Before picking the tools - we need to define the job.
If all we need to do is take a little loose skin from the lower tummy without repairing muscle or moving the belly button higher , the procedure CAN be done under local or tumescent anesthesia.
While I respect your reluctance "to be asleep", let's consider the job that needs to be done in you IF you are to have a chance at a good result. Two full term pregnancies have not only resulted in loose tummy skin but have certainly distended and separated your tummy muscles as well. Failure to tighten your muscles properly would rob you of the flat tummy a properly done tummy tuck can offer.
In my opinion, the tightest and flattest tummies can ONLY be done when you are under general anesthesia because they allow the surgeon to operate on relaxed muscles. While doing it on an "awake" individual (not really since you will be sedated...) will NOT physically allow this degree of movement and tightening.
I am a firm believer of putting myself in my patients' place. Were I to operate on my own wife, I would insist on doing a Tummy Tuck under general - NOT local/twilight/IV sedation anesthesia.
Dr. P. Aldea