In this paper, we develop and analyze a smart digital stethoscope - SkopEdge - to provide reliable remote e-health monitoring with a minimum delay while enhancing overall network performance. SkopEdge initially records the heart sounds from individuals and then senses the quality of the network. Depending on the network traffic, SkopEdge converts the audio clip into an appropriate format before transferring it to remote locations for estimating the number of heartbeats and storage. Towards this, we formulate the link quality along with SkopEdge's current configuration as a Markov Decision Process (MDP) with actions as conversion format selection. The remote server then returns the result, which SkopEdge displays on its screen. Real-time implementations show that SkopEdge works efficiently in all network conditions. Further, audio conversions usually degrade the quality of sound, but our proposed system does not change its primary components. Although SkopEdge exhibits an increase in energy consumption by 79% while converting to lower-quality formats, it also reduces the energy consumption by 99% while transmitting the same, which subsequently results in energy savings. Further, we provide an analysis of the estimated heartbeats in an audio clip by SkopEdge.