To start with your last question, any electrical devices attached to the skin in the area of the chest are going to cause considerable safety concerns. As a practical matter I don't think operating voltages of less than, say 5 V, are going to pose any hazard, especially if the 5 V potential is not directly in contact with the skin, but there may well be some institutional or regulatory paranoia in this area. You would do well to seek expert advice.
As to technical considerations, a Wheatstone bridge is designed to measure voltages without loading the device under test. In your case the no load consideration does not apply, so a Wheatstone bridge is an unnecessary part of the design.
You want to measure a change of about 0.4 ohms in 8 ohms, so about 5%. That is quite a large change and should be easily detectable.
Suppose you use a voltage regulator to generate a fixed 3.3 V supply (just for instance, could be any low voltage). Now place this in series with a 1k resistor and your 8 ohm detector. You will have what is nearly a constant current 3 mA supply across the detector. When the resistance is 8.2 ohms the current will be 3.3 V / (1000 + 8.2) ohms = 3.27 mA and the voltage across the detector will be 3.27 x 8.2 = 26.8 mV. When the resistance is 8.6 ohms the current will be 3.3 / (1000 + 8.6) = 3.27 mA and the voltage across the detector will be 3.27 x 8.6 = 28.1 mV. You have a nearly linear variation in voltage of 1.3 mV in 28 mV or so. You could feed this voltage through a differentiating op amp circuit to detect and amplify the variation.
I don't know what kind of cost considerations you have? If you are able to include a microcontroller in the design the possibilities are limitless. If you want something much simpler and you are limited to discrete components then you will need to be a bit more creative of course.