You're simplifying this far too much. Skin and muscle cells grown in the lab are extremely thin and can thus be vascularized (have your body extend its blood vessels into them) relatively easily. Growing tissue and shaping them into limbs is another matter. There are hundreds of individual musculoskeletal systems in a normal human arm plus thousands of vascular branches to feed those muscles. In addition, each of those muscle groups need different types of nervous connections, depending on whether they're a part of the somatic, sympathetic autonomous or parasympathetic autonomous nervous system. Add that to the intricate bone and tendon structures of the hand, and your picture becomes less easy to accomplish. Current technology doesn't have the necessary advancements to do something that complicated without using stem cells, unless your definition of a limb is a bag made of lab-grown skin and stuffed with lab grown muscles.