The advent of the semiconductor industry and the advancements in communication technologies in the Internet of Things (IoT) era have led to the development of intelligent wearable devices. Additionally, the increased data rates in 6th-generation mobile networks (6G) have spurred the explosive growth of smart systems, particularly in smart healthcare applications. Due to their capability to collect information flexibly and conveniently via sensors, wearable devices have become an integral component of smart healthcare systems. However, their compact structure and reliance on battery power present significant challenges, notably in computing capacity and energy consumption. This paper provides a survey of wearable devices currently employed in healthcare in terms of fundamentals, components, and various use cases and highlights offloading problems for 6G healthcare. Next, we introduce a novel three-layer offloading strategy for wearables-based 6G healthcare applications. The offloading problem and its related constraints are modeled through mathematical formulations and convex optimization problems. Finally, it discusses the challenges and suggests feasible research directions.