An EKG isn't really stressful just so you know that. At worse its just attaching some electrodes and turning on a machine to track how the heart is running. But there are new instruments available, which the vet can just hold at the animal's side to get an EKG reading - with no wires from machine to dog.
Things I would ask before agreeing to the test would include what will be done to the dog during the test (ie find out if its the new equipment your vet uses), and if you do the test will that change the treatment the dog is given.
This site has info on dane heart disease including the inherited disease of cardiomyopathy and links to more sites on the topic
http://www.gdca.org/health/cardio.htm
Hope this helps you!
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