Googling on pulse oximeter brought up a nice site that explains how the fingertip pulse oximeters work - pretty simple concept actually. A comparison of light at two different wavelengths yeilds an indication of oxygen saturation.
It appears that some of the wrist type blood pressure meters are similar to the traditional arm type (sphygmomanometer) in that air pressure is increased until blood flow stops and the air pressure is then reduced while measurements are taken and interpreted to extract the desired information. With the manual type, listening to the blood start to gush past the restriction imposed by the inflated cuff is compared to the manometer reading. In the electronic type a pressure sensor analyzes the subtle variations in cuff pressure, caused by the arteries pushing back, and interprets the data. As I recall, oscillometric is the word used to describe this method.
A basic heart rate monitor looks at the slight but reliable potentials that can be measured at the skin surface that come from the electrical impulses that tied to the beating of the heart. The common chest strap type pushes two electrodes against the chest to make the measurements. There are other types including the kind I see at my gym where it looks at the electrical potential between your hands. Apparently there's enough information in that to reliably derive heart rate. Ramsey electronics sells an EKG kit for $30 or $40. The instructions describe connecting it to an oscilliscope.
All of the electronic methods described have one thing in common - that some pretty sophisticated processing of the raw data that is gathered, is required. Pressure or voltage levels are extremely low so there is lots of noise or interference.
I mention this stuff so that you might do a little reading to help guide you. I wonder if you couldn't use a sound card and some audio analysis software as a tool.